Madly in love and oblivious to social stigmas and the calamity of World War II around them, Carl Hatch, a black-American soldier, and Sheila Bennett, his white, British sweetheart, caress openly in a Bristol pub. Their kiss provokes a minor racial scuffle. The next evening Hatch sits at the piano in Bennett's home singing "America, the Beautiful" (". . . and crown thy good with brotherhood") while his sweetheart looks at a photograph of an American lynching.

"The File on Jill Hatch," a three-part drama that debuts tonight on channels 26 and 32 at 9 and continues the next two Tuesday nights, traces this interracial match and its repercussions on Carl and Sheila's daughter, Jill. Like the raucous pub incident and the singing the next night, the three hours are properly packed with romantic blindness, and catalogue 40 years of racial attitudes.

Many writers have explored interracial relationships. James Baldwin's "Another Country," David Bradley's "The Chaneysville Incident" and Eugene O'Neill's "All God's Chillun Got Wings" come to mind. White-black duos have slipped into some musicals such as "No Strings," and some television slapstick, such as "The Jeffersons." But serious dramatic treatments have been few. "The File on Jill Hatch," written by Kenneth Cavander, does not penetrate any new realities, yet it makes a solid contribution.

The show is a joint venture between the British Broadcasting Company and the Public Broadcasting Service's New York outlet, WNET. The result is strong performances and evocative scenes. Sometimes the drama is frank, as when the soldier's mother reveals middle-class black opposition to the marriage. It can also be faint and cliche'd, as when the daughter, in African dress, does her revolutionary's pout number in rejecting her father's success.

The framework for the show is an investigation into the causes of the 1981 riots in Bristol's West Indian community. William Bennett, the British uncle of Jill Hatch, and a detective, narrates throughout the three hours. Testifying in front of a police board about his niece's involvement in the riots, he delves into her parents' story, which is shown in flashbacks.

The lives of Carl Hatch, played by Joe Morton, and his wife Sheila, played by Frances Tomelty, are inextricably linked with the momentous events around them: World War II, the ironclad segregation that existed in the American South of the 1940s where they couldn't make a home, the subtle prejudice of New Haven in the l940s and l950s, the churnings of the 1960s civil rights movement, and the recent riots in Britain's immigrant communities. Tonight's episode goes from l943 to 1945, the year the Hatches start their lives in America.

Against a four-decade panorama, the Hatches build up their relationship, pull it apart and build it again. At times they seem madly mature, at times just mad, and at times it's the world that has crazy rules and won't let them alone. The story is strongest when the sociology erupts, as it does in moments both icy and passionate. The chilly disapproval of Hatch's mother, played magnificently by Gloria Foster, is electric, as she reigns over her Birmingham, Ala., dynasty and lets her son's less-educated British bride know that the Hatch family is destined, as well as talented.

There's the explosive argument ignited by Hatch, then a doctoral student at Yale, when he shows up at his wife's receptionist job at a New Haven legal firm. She keeps him waiting. She fails to introduce him to her coworkers. Then she is fired for being married to a black. Afterwards, at home, they learn that they may have fussed with their parents, but they haven't exposed the pain of a partner's prejudices, the real fear of an interracial coupling. When they do, a maturity takes over their characters and the production.

The story is well-served by its presentation not only as romance and sociology, but also as a detective story, as the role played in the riots by Jill Hatch unfolds. Jill, played as an adult by an energetic Penny Johnson, finds herelf on the chronic mulatto quest for identity. The slow, official tone of Tim Woodward's Detective Bennett gives the story some of its distance, but also gives analysis that many of the characters aren't loose enough to provide.