The Brooklyn-born son of immigrants (his father was from Lebanon, his mother Israel), Dishy began performing at a Catskills resort. After completing his studies at Syracuse University, he landed his first stage role replacing James Komack in the original production of the Broadway musical "Damn Yankees" in 1955. Drafted several months later, he spent his military career performing in the revue "Rolling Along". After being discharged, Dishy returned to NYC and quickly fell in with the Second City troupe whose members included Paul Sills, Barbara Harris, Avery Schreiber and Severn Darden. Honing his comedic skills, Dishy began to appear frequently in cabarets, stage revues and the NBC comedy series "That Was the Week That Was" (1964-65). He enjoyed a rare romantic lead opposite then-newcomer Liza Minnelli in the musical "Flora, the Red Menace" (1965) before segueing to features.
His lips ready to curl around a wisecrack in middle-class frustration, Dishy perfectly embodied Neil Simon/sitcom shtick, hence his numerous guest appearances on TV sitcoms and comedic roles in features. He debuted in films as the husband of a woman kidnapped by a frustrated mailman in "The Tiger Makes Out" (1967) and subsequently essayed an usher with a talkative blind date in "Lovers and Other Strangers" (1970), the Vice President in "First Family" (1980), the father in the film version of Simon's "Brighton Beach Memoirs" (1986) and a psychiatrist in "Don Juan DeMarco" (1995). In a rare lead, he excelled as a man attempting to cancel the order for a hit man to murder his wife in "I Wonder Who's Killing Her Now" (1976), but he offered one of his best screen performances as a conflicted school principal torn between his family and a schoolteacher in "Judy Berlin" (1999).
The busy actor has also continued to nurture his stage career. Since the 60s, he has alternated between comedies and musicals, including turns in Herb Gardner's "The Goodbye People" (1968) and "Story Theater" (1971, which also led to a syndicated TV series). In 1977, he won particular praise (and a Tony Award nomination) for his supporting turn in "Sly Fox", Larry Gelbart's modernization of "Volpone". Dishy turned serious for the first time in Jules Feiffer's "Grown-Ups" (1982) and has since displayed his mettle in roles as varied as a waiter (alongside Fyvush Finkel) in "Cafe Crown" (1988) and a retired button-maker wooing a Holocaust survivor in "Blue Light" (1994) and its revision, "The Shawl" (1996).