Rasche graduated from Elmhurst College in 1966; his grandfather was also an alumnus. Coming from “a long line of Evangelical and United Church of Christ ministers”, he attended the University of Chicago Divinity School for two years, then quit. He did, however, receive a graduate degree in English from University of Chicago.

Rasche met his future wife Heather Lupton after he moved to New York City in 1976. She has taught acting at University of California, Santa Barbara. Lupton made a guest appearance in the series Sledge Hammer as Hammer’s ex-wife. They have three children. Rasche owns a house in Santa Barbara, California.

He began appearing on television and films in 1977, making his film debut in 1978 in An Unmarried Woman, directed by Paul Mazursky. The following year, he had a small part in Woody Allen’s Manhattan.

He played a terrorist in the 1983 television film Special Bulletin. He appeared on the Miami Vice episode “Bushido” (first aired November 22, 1985) as a KGB agent attempting to capture a former colleague of Lt. Castillo (Edward James Olmos). During his subsequent starring role on Sledge Hammer! his character often made jokes about Miami Vice.

He played Parnelli, one of two corrupt narcotics police officers, in the 1989 Tom Selleck crime drama, An Innocent Man.

Rasche was lead character Buddy Wheeler in the 1990 Biker Comedy Masters of Menace.

Rasche played the role of Ted Forstmann in the 1993 made-for-television movie Barbarians at the Gate, about the leveraged buyout (LBO) of RJR Nabisco.

Rasche had a leading role in the 1997 Columbo episode, “A Trace of Murder.”

He had a major role in the 2009 satirical political comedy In the Loop, as a US official pushing for an invasion of an unspecified Middle Eastern country.