Cohen was diagnosed with multiple sclerosis in 1973. His condition worsened over 30 years. During that time Cohen was also struck with two bouts of colon cancer in 1999 and 2000. He has written an autobiographical account titled, Blindsided: Lifting a Life Above Illness: A Reluctant Memoir.
Cohen married television personality Meredith Vieira (co-anchor of NBC's Today Show) on June 14, 1986. They live in Westchester County, New York. They have three children.