How to deal with husband that always flips things to evade lies and manipulates me in order to stay with me?

I found an inappropriate message from my husband in his archived Facebook messages. When I confronted him, he denied it and acted defensively, claiming that he would never try to contact her since he knows her through his ex's family. He even suggested that I might have sent the messages and threatened to tell my family that I'm trying to spew a false narrative about him because I am possibly cheating on him. Knowing fully well that that's false and I would never do such a thing, but he knows he can control me by threatening to tell lies to my family. The messages said “I want to f*** you,” and "are you home?". He has done this many times before and has cheated many times, I just don't know what to do anymore since I feel trapped.

I've told him I'm open to a peaceful breakup and don't want anything from him. There's no point in staying together if he continues cheating. I don't want my family to know that he cheats either, so I prefer not to tell anyone even if we do separate.

How to deal with husband that always flips things to evade lies and manipulates me in order to stay with me?
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