PATRICIA AND Richard Fiske are like many couples who have chosen to have it all: children, careers and companionship.

But they are, they say, the country's only museum directors married to each other. And they live in the arcane and complex labyrinths of the museum world, which spins between the planets of scholarship and ballyhoo.

Richard Fiske is director of the Smithsonian's Museum of Natural History. He has more than 62 million bugs, bones, boulders, artifacts, plants and jewels to keep, a large building on the Mall, plus the dinosaur's share of the new Smithsonian Support Center at Silver Hill and a staff of 506. Five million visitors a year come to the museum, second in popularity only to the Air and Space Museum.

Patricia Fiske is director of the Textile Museum, one of the only two or three of its kind in the world. She presides over 1,000 rugs, 10,000 other textiles and a staff of 18. Her domain is a museum, visited by 33,000 people each year, converted from two former mansions in one of Washington's ritziest sections, Kalorama.

Tall, thin, with strong bones, broad chins and smiles to match, the Fiskes stand above the crowd. Except for the hair, they could be twins. Even their gestures and stances are alike. For a photograph, they unconsciously held their hands and crossed their legs in the same way. And they are alike in their enthusiasms.

They shop together on the way home from work. He fixes breakfast (mostly cold cereal and coffee, which she alleges he warms up for three days). She does the rest of the cooking, "or we just wait around for supper to happen." He does all the carpentry and repair work. Their son Peter, 17, picks up the pieces, washes the car and alternates with his father in taking out the trash; he also works one day a week as a receptionist at the Textile Museum. Their daughter, Anne, 20, is studying political science and East Asian studies at Wellesley.

"It's a good thing the children have always been independent and can be trusted to be independent," said Patricia Fiske, "because Dick and I usually leave the house before 7 and come home after 7. We like to have an hour in the office before and after everyone else comes in. We usually work one day out of the weekend. If the children are both out of town, we declare it adults' night, and go out to Childe Harold for drinks and dinner."

Except for reading, neither as a rule brings work home.

Richard Fiske broke the rule a few winters ago, according to one colleague. Fiske, a geologist who specializes in the study of volcanoes, went out to his garage and built a wooden Jell-O mold and filled it with a clear gelatin. When the mold was set, he turned it upside down on a board and spiked it with a filling of red syrup. As he'd expected, the red syrup erupted along a ridge line, considerably down from the center.

And that's how he demonstrated his theory of how the volcanic islands of Hawaii were formed. The model also helped predict where new volcanoes will erupt in Hawaii.

In the home movie Richard Fiske made of his experiment, the last reel shows the Fiske children finishing off the Jell-O.

THEIR OFFICES are more reflective of their interests and tastes than is their house. But then, they spend more time in their offices.

Richard Fiske's is meticulously decorated with modern furniture and a sampler of the museum's wares. He's proudest of the wall of photos he's taken of volcanoes in Hawaii and St. Vincent island in the Caribbean. He and a colleague, Tom Simkin, are writing a book, about a famous volcano, Krakatau, in what is now Indonesia, to be published by the Smithsonian Press.

The Navajo blankets on another wall, he explained, were bought by his grandfather, "an itinerant glass salesman, who traveled in the West . . . Indians used to sell them at train stations." A meteorite sits on the top of a wall of shelves, along with Central American pottery, alabaster figures, a set of bound Smithsonian annual reports, a Japanese doll and a flourishing cactus.

Patricia Fiske's office is comfortable and casual, far less studied than her husband's. The fireplace has an Adams neoclassical mantel. On one recent day, an elaborate Saudi Arabian costume was spread across the sofa. Books, magazines, papers and pictures of the Fiskes' children are there in profusion. On the mantelpiece is a plaque that says, "The best man for a job is often a woman." She laughs about it. "The chairman of the museum's board gave it to me."

The Fiske house, Patricia Fiske likes to joke, "is chiefly furnished with chairs from eastern universities--Wellesley, Princeton and Johns Hopkins." The house is small, and oriental rugs carpet the floor. Jordanian pillows are spread over the sofas. A Moroccan shawl hides the dog scratches.

"Penny, the dog, tastes every textile I bring in the house," said Patricia Fiske. "She liked the red Moroccan saddle bag, but she just loved the Moroccan basket. She gets up on her hind legs to plead to lick it. That's better than a rug collector friend of mine. He has a dog who's such a connoisseur that he defiles any rug made with commercial dyes. The dog is infallible at telling which are natural."

THE FISKES spent their first year of marriage in Japan, where Richard was a post-doctorate fellow at the University of Tokyo, studying volcanoes. Later, they lived in Hawaii for a year, and their son Peter was born there.

In 1976 Richard was part of a team that had set out to measure the summit of Soufrie re, a volcano in Guadeloupe. They were halfway up, he said, "when all of a sudden black clouds boomed out. The earth shook. Great rocks, as big as a car, came rolling down the mountain. I was really scared--all it takes is just one rock to finish you off.

"None of us were wearing hard hats. We piled into the car and roared down the mountain." No one in his party was hurt, but members of another group were.

His other close call came in 1979, when he was in a helicopter crash on St. Vincent. "The air was warm and the air currents sent it spiraling down in an uncontrolled descent. Fortunately, we crashed into a heavily plowed field and that broke our landing," he remembers.

Despite the close calls, Fiske almost shrugs on the risks involved in the study of volcanoes.

"The risks are there, but I count them as within acceptable limits. After all, you can be finished off while crossing the street," he said.

THE FISKES share their museum problems as well as their domestic ones. "Because Pat's museum is smaller, and fewer people are involved, it's easier to try out new ideas at hers," Richard Fiske said.

Recently, when an auditor's report showed problems with the way the Natural History Museum's gem collection had been managed, (a situation that began before Fiske's tenure), the Fiskes spent many hours discussing the ethics of the way museums accept and sell objects from the collections.

And, on a less theoretical level, when Patricia Fiske, then a curator at the Textile Museum, installed her exhibitions, Richard Fiske, as an unpaid volunteer, did much of the carpentry.

From 1964 to 1976, Richard Fiske was with the U.S. Geological Survey. He credits his wife for his decision to switch to the Smithsonian. "After I saw how much he enjoyed my work," she said, "I told a friend at the Natural History Museum that I thought Dick would like working there. Not long after, they offered him a job."

He had wanted to be a geologist since he was 12. "It was more the romance of being a geologist that appealed to me--I didn't collect rocks and minerals as a child. I had an uncle who was a geologist with an oil company in Caracas, Venezuela. After I found out that his life wasn't really that romantic, it was too late--I was hooked on geology."

As a child, Fiske worked most weekends for his father's catering firm, then the best known in Baltimore. Even today, he enjoys selecting the menus and planning the parties at Natural History--especially the elaborate sushi and such for the opening of the Japanese ceramics exhibit.

He received a bachelor's and master's degree in geological engineering from Princeton University and a doctorate in geology from Johns Hopkins University in 1960.

He came to the Smithsonian as a vulcanologist with the museum's Department of Mineral Sciences in September 1976. He soon became chairman of exhibits and a favorite lecturer. Four years later, in 1980, he was named director.

As director, a principal concern has been in setting up a system of review boards, which are currently working all the way through Natural History museum. "They're looking at the way we do everything, making recommendations on staff and procedures. As a vulcanologist, I'll be reviewed as well." Fiske said the review boards were functioning before the controversy about the gem collection blew.

His latest project: overseeing the moving of 20 million objects from Natural History to the new Silver Hill Support Center, the Smithsonian's enormous new facility for storage and research.

PATRICIA FISKE became director of the Textile Museum last September. "I would never hire a curator with my lack of credentials," she said with a wry grin. "And I certainly would never counsel my daughter to be as lackadaisical about preparing for a career as I was.

"My parents thought that my life would be like theirs. My father is a doctor, my mother is a wife. One brother is an architect, another is a doctor. They didn't expect me to be anything. They sent me to Wellesley College because I was a bright girl who deserved an education. I majored in mathemetics with a few courses in art history--my roommate was an art major--and literature, which I enjoyed more. If I'd wanted to go on to graduate school to become a teacher, I'm sure they would have helped me. But I didn't have a strong interest in going. Instead, I went to work as a research assistant in Johns Hopkins University aeronautics department."

One day, in the cafeteria at Johns Hopkins, Richard Fiske noticed her and asked to be introduced. They'd met before--when she was in the eighth grade and he was the 12th grade and in the same school.

They were married in 1959, and promptly went off to Japan so he could study volcanoes.

She taught mathematics and worked as an editor for a Japanese art critic, and she took the opportunity to learn about oriental art. "Textiles are at least as important in the Far East as paintings and sculpture," she said. "That's where I began to be interested in textiles. Something about the structure, the warp and the woof, appealed to my mathematical mind."

When they came back, she worked at Hopkins again. "But I would walk by the Baltimore Museum of Art. Finally, I went in and applied for and got a job as a curatorial assistant." She stayed there for a year, before they moved to Washington. That was when she became a volunteer at the Textile Museum.

Andrew Oliver, now head of museum liaison at the National Endowment for the Arts, was Patricia Fiske's predecessor.

"Pat came to her present job through the side door, in the 19th-century manner, where a curator at say, the British Museum, had likely been a diplomat or naval officer, with a classical education, who had acquired a knowledge of some regional culture."

She worked at the Textile Museum two years as a volunteer docent and as head of the docent program. She became a staff member in 1973; was coordinator for the Irene Emery Roundtable on Museum Textiles and edited its five volumes on textiles.

Patricia Fiske made her name with the big Moroccan show several years ago, one of the most popular Textile Museum exhibitions. Probably as important, she went to Morocco, with two museum trustees, to research for the show. Fiske edited the catalogue for the show, as well as writing one of the major pieces for it.Lilo Markovitch, head of the museum shop, also started as a volunteer. "When we started in the '60s women were volunteers because we had families. The Textile Museum was one of those places where you could bring your child into the office if the maid didn't come, and you had no one to babysit. Both she and I as working mothers had to juggle our lives. And if a child was sick, there was no hesitation as to priorities. She was very fortunate in having her husband support her. You can't have a family and a career unless you're married to an mature man. Someone who'll help."

Patricia Fiske agrees. "Dick has always encouraged me in many ways. When I was in Morocco, Dick took care of Peter, and, of course, Peter came down with tonsillitis. And Dick had to take time off to be with him. Usually, I was the one who took care of the sick child--I had a sofa in my office to put them on if all else failed. At least at the Textile Museum, everybody on the staff could do that sort of thing. I wish there were more jobs with flexibility."

The Fiskes think the reason they get along is that they are flexible. Or, as Patricia Fiske said, "The great thing about Dick is that he isn't uptight about who does what. The day is past when mother is fulfilled by scrubbing the baths."