Holmes was born David Goldstein in Northwich, Cheshire, England. His father, Leonard Goldstein, was a United States Army Warrant Officer and bandleader, his mother, Gwen, was English, and both were musical. Holmes has dual American and British citizenship. The family moved, after a few years in Northwich, to the northern New York City suburb of Nanuet, New York, where Holmes grew up and attended nearby Nyack High School and then the Manhattan School of Music (majoring in clarinet). Holmes' brother, Richard, is an opera singer based in New York City and is the principal lyric baritone of the New York Gilbert and Sullivan Players, sings roles with regional opera companies, such as Glimmerglass Opera, Lake George, and Virginia Opera, among others, and has appeared at the Metropolitan Opera.