Bernstein started his career as a concert pianist and began composing and arranging for the Army Air Corps Radio Shows during World War II. His film career was stalled during the 1950s when he was "gray-listed" for his refusal to identify communists in the film industry.
In addition to his film work, which also included scores for The Great Escape, True Grit, Airplane!, Ghostbusters, A River Runs Through It, and The Age of Innocence, Bernstein composed works for concert stages and wrote the scores for two Broadway musicals: How Now Dow Jones (1967) and Merlin (1983). He also wrote much of the dance music for the Moose Charlap-Jule Styne-Carolyn Leigh-Betty Comden-Adolph Green adaptation of Peter Pan (1954), which starred Mary Martin.
The composer received Tony Award nominations for How Now Dow Jones and Merlin, and he earned a total of 14 Academy Award nominations for his film work. In 1964, he won an Emmy Award for The Making of the President: 1960.
Bernstein is survived by his wife, two sons, two daughters, and five grandchildren.