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Martin had been a rather terrible father to Charlie in the past, which made Charlie hesitant to see him.
Martin showed up to visit Charlie and was noticeably kinder and gentler than he supposedly was. He tried to convince Charlie, via a few lies, that he'd always been this way. It almost worked, but in the end Martin came clean that he'd not always been the best father. Martin claimed that he was on his own now and was in need of a place to stay. He then made a promise to Charlie that he will do the best he can to be a good father this time around. ("Charlie's Dad Visits")
Charlie Goodson - His son, though they don't always see eye to eye due to things that's happened in Charlie's youth (such as lies and other things). He attempts to get Charlie to go back to church, with little luck.
Martin Sheen is Charlie Sheen's real life father.