Alexander met her first husband, Robert Alexander, in the early 1960s in New York City, where both were pursuing acting careers. They had one son, Jace Alexander, in 1964, and the couple divorced a decade later. Alexander had been acting regularly in various regional theaters when she met producer/director Edwin Sherin in Washington, DC, where he was artistic Director at Arena Stage. Alexander starred in the original theatrical production of The Great White Hope under Sherin's direction at Arena Stage prior to the play's Broadway debut. The two became good friends and, once divorced from their respective spouses, became romantically involved, marrying in 1975. Between the two, they have four children, Alexander's son Jace and Sherin's three sons, Tony, Geoffrey, and Jon.