Ping!
I don't think I've ever seen a tv program or movie about a schizophrenic family. It might be interesting, though, especially if it emphasized the struggles of the family trying to negotiate the mental-health system under Obamacare ...
Tom Barnaby in “Midsomer Murders” is a good father and husband. Christopher Foyle in “Foyle’s War” is a good father. (His wife died prior to the series’s timeframe.) His driver, Samantha Stuart, has a loving father and uncle, both Church of England priests, who occasionally appear in episodes. Don Johnson’s successful characters, Sonny Crockett and Nash Bridges, were both divorced, but both were caring and involved fathers, especially Bridges.