Berman has been married twice, to engineer Victor Berman in the 1960s, and to molecular biologist Peter Young from 1976 to 1999. From the second marriage she has a son, Jason Asher Young (born 1979), a physicist.
During the 1980s, Berman was diagnosed with breast cancer. The experience made her more focused in her life and her career, and interested in supporting other women who face the same diagnosis.