Her father, Joseph, was an advertising salesman; her mother, Marie Stapleton, was a concert and opera singer, and music was very much a part of her young life. Young Jeanne was a singer as well, which might be surprising to those who knew Ms. Stapleton only from “All in the Family,” which opened every week with Edith and Archie singing the song “Those Were the Days.” Ms. Stapleton’s screechy half of the duet was all Edith; the actress herself had a long history of charming musical performances. She was in the original casts of “Bells are Ringing” and “Damn Yankees” on Broadway in the 1950’s, and “Funny Girl,” with Barbra Streisand, in the 1960’s, in which she sang “If A Girl Isn’t Pretty,” and “Find Yourself a Man.” Off Broadway in 1991, she played Julia Child, singing the recipe for chocolate cake in the mini-musical “Bon Appétit.” On television, she sang with the Muppets.Here's the audio of Stapleton singing "If A Girl Isn't Pretty."
ADDED: Here's an interview with her from 2000. At about the 6-minute mark, she talks about first meeting Carroll O'Connor when the 2 were cast in an episode of the TV show "The Defenders."