He has been known to be abusive to Emily, and is sometimes abusive to her daughter, Alex. It is presumed that he became abusive because of his experiencing it early on in his life (parents fighting, abuse from his father and/or mother, etc.).
In The Lexicon of Love (1) at Alex's house, Emily and Chad get in a fight, and Alex ends up hitting her arm against the table, and she and Paige head back to Paige's house.
In The Lexicon of Love (2), Chad and Emily are back together, despite the fight and Chad throwing Alex under a small table
In Don't You Want Me? (1), Chad has run up thousands of dollars in credit card debt and hasn't been paying the rent. He is arrested and taken to jail.
In Don't You Want Me? (2), Emily bails out Chad with Alex's money that she had earned while stripping.