Henry first ventured into films co-writing (with Theodore J. Flicker) the story and screenplay for "The Troublemaker" (1964), a quirky, independently produced little comedy in which he also acted with members of The Premise, a NYC improvisational theater group which he had joined in 1960. After the success of "Get Smart", he returned to features as the co-scripter (with Calder Willingham) of Mike Nichols' "The Graduate" (1967), a major hit and one of the signature films of the decade. Suddenly on the A-list of Hollywood screenwriters, Henry went on to collaborate on some of the more popular, influential and/or notorious films of the late 60s and early 70s including Nichols' "Catch-22" (1970) and the Barbra Streisand vehicles "The Owl and the Pussycat" (1970) and "What's Up, Doc?" (1972). His assignments tended to be hip adaptations of popular plays and countercultural novels that skewered middle American values. His last major hit was the amiable 1978 remake "Heaven Can Wait" (based on 1941's "Here Comes Mr. Jordan") which, ironically, he co-directed and co-produced with Warren Beatty but did not script.

Henry's writing has declined drastically since the late 70s, both in quantity and, in the view of most critics, in quality. His first credit as the sole writer and director of a feature was "First Family" (1980), a poorly received satire of Presidential politics. Four years passed before Henry's next screenplay, "Protocol" (1984), a disappointing Goldie Hawn vehicle with Capra-esque aspirations. While his screenwriting career waned, his career as a character actor thrived. With his slight physique, thinning hair and generally bookish appearance, Henry was no one's idea of a matinee idol but he gained increased visibility on film and TV nonetheless. He benefited greatly from the young following he gained as a favored frequent guest host on "Saturday Night Live" since its 1975 inception. Henry's film roles include the fastidious and sympathetic Mr. Farnsworth who meets an unfortunate fate in Nicolas Roeg's "The Man Who Fell to Earth" (1976), a nervous accountant on the outs with the mob in John Cassavetes' "Gloria" (1980) and the kindly priest who runs the mission at the local leper colony in "Tune in Tomorrow" (1990). He appeared as himself in Robert Altman's "The Player" (1992), pitching a sequel to "The Graduate", and gave a brief amusing turn as a dedicated weekend fisherman in the director's "Short Cuts" (1993).

Henry made a triumphant return to screenwriting with a well-received adaptation of Joyce Maynard's novel, "To Die For" (1995), a hard-edged satire on the nature of American celebrity headlined by Nicole Kidman and directed by Gus Van Sant Jr.