Two infants and a 20-year-old woman were killed in a fire yesterday that destroyed three units and damaged 12 others in a District Heights apartment building.

Elizabeth Kimberly Faber was found dead in the hallway outside the second-floor apartment where she was staying with a friend after she had apparently tried to re-enter the apartment to save one of her children and her friend's child, fire officials said.

Faber's 7-month-old daughter, Katie Irene, and 20-month-old David Willoughby were found dead on the livingroom floor. Fire officials determined that the blaze, which occurred at 1948 Rochell Ave., was caused by a cigarette burning on a living-room couch.

Dorothy Willoughby, mother of the boy, was treated for first- and second-degree burns at Prince George's Hospital and released, according to a hospital spokesperson. She fled the fire and then attempted unsuccessfully to re-enter the apartment. Faber's 3-year-old daughter, Kelly, escaped the fire unharmed.

The blaze, which caused $150,000 in damage, forced nine families to evacuate the Walker Mill apartment building. Most of the families were relocated in other apartments in the complex, according to Alice Kipper, resident manager.

The fire began at about 7:30 a.m. Fire officials said the apartment building did not have smoke detectors. All multiunit dwellings in the country are required to have the detectors by 1978.