Lauren Bianca Haymon, who turns 2 tomorrow, is by all measures a remarkable child.

She has big cheeks and wide, searching eyes. When she wants to watch television, she picks up a remote control unit and gestures toward the screen. When someone says goodbye, she smiles and blows a kiss.

Her mother, Carolyn Haymon, says she often is surprised by her daughter's perception, inquisitiveness and stubbornness.

But Lauren was born with two significant handicaps. She has a rare combination of heart defects that, although partially corrected by surgery, may become life-threatening. And she was born with Down's syndrome, a genetic affliction that results in at least mild retardation.

Down's syndrome is relatively uncommon. According to national medical statistics, it can be expected in one out of 885 births to mothers who are 30 years old.

But among children of mothers who are 35, it occurs in one out of every 365 births, and the odds continue to increase with the mother's age.

Lauren's case is remarkable for other reasons. Her parents say that if they had known she would be born with Down's syndrome, they would have aborted the pregnancy. They say their doctor failed to recommend a test that would have revealed the problem, and they have filed a $2 million lawsuit alleging medical malpractice.

It is believed to be the first of two "wrongful birth" suits filed in the District by parents of children with Down's syndrome.

When Carolyn Haymon became pregnant at age 34, her husband Bill urged her to have an amniocentesis performed, the couple said. The medical test, in which a sample of the fluid surrounding the fetus is extracted from the mother's uterus with a long needle, can detect Down's syndrome before birth.

Carolyn Haymon did not have the test performed. She said her doctor told her the procedure was unnecessary, but her doctor disputes Haymon's account. Lauren was born on Feb. 9, 1986, five months after Haymon had turned 35. Haymon learned then that her daughter had Down's syndrome.

Besides the initial shock, Carolyn Haymon said, there was the added trauma of questions asked by others after the birth -- such as one from a nurse at the Columbia Hospital for Women -- about whether Haymon planned to keep her daughter or put the baby in an institution.

Dr. Marciana Wilkerson, Haymon's obstetrician, declined to comment on the case. She said in a deposition that she had informed Haymon about the risks of having a child with Down's syndrome and that Haymon decided not to have the test despite her husband's insistence.

During a recent interview, Bill Haymon, a 41-year-old financial planner, expressed conflicting emotions. He said his wife would have had an abortion had they known of Lauren's condition. But, he said, their lives have been much richer since Lauren's birth.

"She's a treasure," he said.

Carolyn Haymon quit her sales job with a long-distance telephone company when Lauren was born, because, she said, she did not want to leave the child with a baby sitter.

"No one could work with her or love her like me," she said. "When I realized this baby needed me more, I could not justify leaving her in the care of somebody else."

The Haymons say they have incurred more than $100,000 in medical bills, mainly for treatment of Lauren's heart condition. The Haymons' attorney, Aaron M. Levine, said they face more than $1 million in therapy expenses. Most of these costs are likely to be covered by health insurance, Bill Haymon said.

Lauren was born with a combination of defects that left her heart without most of the inner wall that separates the four chambers. It is common for children with Down's syndrome to have heart problems, but Lauren's cardiologist, Dr. Stanley Beder, said her combination of ailments is "extremely rare."

Lauren's heart valves leak. Her heart is unable to pump enough blood to her lungs. She has been treated for congestive heart failure since birth, and she probably will stay on medication indefinitely.

Last month, surgeons at Children's Hospital performed a 12-hour operation to correct most of the defects, but Beder said Lauren still could face major surgery in the future.

Also, Lauren has a slight hearing impairment in one ear. Because of her mild retardation she can speak only a few words, but she has learned hand signals and signs for a few dozen phrases and ideas.

The Haymons' lawsuit has raised complex issues. It initially was dismissed by a Superior Court judge, but it was reinstated by the D.C. Court of Appeals. The appellate court ruled that parents of a child born with Down's syndrome can sue for extraordinary health care expenses under a legal theory known as "wrongful birth."

In virtually every state in which the issue has been considered, the appeals court said, parents have been allowed to sue for special expenses in caring for a handicapped child when a doctor's alleged malpractice deprived the parents of the chance to consider an abortion.

Today, a trial is scheduled to begin in D.C. Superior Court in a similar case, in which the parents of a child with Down's syndrome are seeking millions of dollars in damages from a local obstetrician. The two suits are being watched closely by area obstetricians.

Dr. Alan B. Weingold, chairman of obstetrics and gynecology at George Washington University Hospital, said physicians "are very much aware" of the prospect of litigation when a mother delivers an abnormal child. The American College of Obstetricians and Gynecologists has issued guidelines on advising women 35 and older about the risks of Down's syndrome and other defects and informing them of various tests to detect the problems before birth, he said.

In her deposition, obstetrician Wilkerson said that an obstetrician's duty is to inform a patient of the increased risks of having a child with Down's syndrome as the mother's age increases, to describe amniocentesis and to let the patient decide.

Carolyn Haymon, in a deposition, said that Wilkerson told her there was only a 1-in-800 chance of having a child with Down's syndrome because she had not then reached her 35th birthday and that there was no need to have the test.

Levine, the Haymons' attorney, said the guidelines set by the college of obstetricians and gynecologists apply to women who are 35 and older at the time of delivery. He added that Wilkerson did not mention her advice about amniocentesis in Carolyn Haymon's medical records.

In her deposition, Wilkerson said she did not mention the advice because she and Haymon were friends. She contended that Haymon decided not to undergo the test because of fears that it would be painful.