In 1994 Beverly was the first woman to become Chair of the Lincoln Center for the Performing Arts. She was also the first former artist to hold the position.
Beverly and her husband had two children. Their daughter, Meredith (nicknamed Muffy), was born deaf in 1959. Their son, Peter Jr. (nicknamed Bucky), born in 1961, has autism.
In 1956 Beverly married Peter Greenough, associate editor of the Cleveland Plain Dealer. Greenough was in the process of divorcing his wife when he and Beverly met. He brought three children to the marriage.
Beverly's nickname was Bubbles.