By the 1930s he was an established comic actor, often in main roles as leaders of buffoon duos, well-meaning policemen, or more substantial "uncle types".

He was well known for his ability to perform "the colossus with feet of clay", apparently solid and superior characters – both sympathetic and unsympathetic – who fall apart by the end of the film.

Among his best-known serious performances are his mean-cultivated informer type in Afsporet (1942 – Derailed); his leader af a children's home, a sadist with shattered nerves in the social film Kampen mod uretten (1949 – The Struggle Against Injustice) and his two portraits of alcoholics in Ta’ hvad du vil ha’ (1947 – Take What You Want) and Café Paradis (1951).

He was an active public figure, appearing at the opening of exhibitions, and freely providing the press with interviews about his ideas and projects.

In 1948, Schønberg won the Bodil Award for Best Supporting Actor for his role as Oscar Bergholtz in the film Ta', hvad du vil ha' [da] (English title: Take What You Want).