He is perhaps best known for his role as "Martin" in the 1983 NBC miniseries V and its 1984 sequel V: The Final Battle. He reprised his role in the pilot episode of V: The Series but was killed off by the end of the episode. He returned later on in V: The Series as Philip, Martin's twin brother.
Ashmore is also known for his film appearances in the 1980 hit comedy film Airplane! and its 1982 sequel Airplane II: The Sequel. He also appeared in the 1979 film Parts: The Clonus Horror and has made guest appearances on various television shows including Happy Days, Battlestar Galactica, Touched by an Angel and The West Wing. In 2010 he had a recurring role in season 4 of The Guild web series.