He was born to Jay Frederick Reeve (1893–1956), a lawyer, and his wife, née Josephine Medill Patterson (1913–1996), a reporter and airplane pilot. His parents divorced in 1944, and his mother married painter Ivan Le Lorraine Albright in 1946.
He is the former husband of Madeleine Albright. Two additional children were born to this second marriage, Adam and Blandina (known as "Dina"). His great-great grandfather, Joseph Medill, owned the Chicago Tribune and had been elected mayor of Chicago.
Albright attended Williams College.
He met Madeleine Jana Korbel when she spent a summer working at the Denver Post. They had three daughters: Katie and twins Anne and Alice.
After he left Madeleine for another woman, the couple divorced in 1982. Albright remarried Marcia Kunstel.
They own Flat Creek Ranch in Jackson Hole, Wyoming.
