He married Marjory Perkins in 1953; the couple had nine children, including actor Eamonn Roche and Emmy Award-winning writer/producer Sean Roche. They divorced in 1981. Eugene Roche remarried in 1982 and remained married to his second wife, Anntoni C. Roche (née Bratman), until his death in 2004.

Roche made his Broadway debut in 1961 as a bit player in the play Blood, Sweat and Stanley Poole with Darren McGavin and went on to appear in Mother Courage with Anne Bancroft in 1963, and in The White House with Helen Hayes in 1964. Television comedy would become his forte with recurring roles on Soap, as Christine Sullivan's father on Night Court, Webster, and Larry Appleton's abusive boss on Perfect Strangers. Roche appeared as "Pinky Peterson", one of Archie Bunker's buddies, on several episodes of All in the Family, in mostly comedic episodes. He had supporting parts in such feature films as The Late Show (1977), Foul Play (1978), and Corvette Summer (1978).

Roche did play dramatic supporting roles as well, often playing deceptively ordinary men who are shown to be capable of ruthlessness, menacing violence or disturbing perversity. In Murder, She Wrote, he played a very bad cop who attempts to kill off Jessica Fletcher, and as a Criminal mastermind posing as a Catholic bishop in the film Foul Play. He appeared in two episodes of Kojak. In 1977, he appeared in "Never Con a Killer" (the pilot episode for The Feather and Father Gang). He played alien Jor Brel in an episode of Star Trek: Voyager called Remember.