He cheated...because he thought I was cheating

So I’m writing this holding my seven month old daughter. Rocking her to sleep...trying to hold my composure together. He cheated. He admitted it. He said that he thought I was cheating because I wasn’t being affectionate and I had mentioned I didn’t finish while we where having sex as much as I used to. He said he saw I was talking to other women. (In a non flirty way) because I was just trying to make more girl friends...but he assumed since I like women as well that these where all signs that I was cheating. So being as angry as he was he got on a chat room specifically to have phone sex with another women. He said he wanted to masturbate to her and with her but he couldn’t bring himself to do it. He wanted to get back at me even though I wasn’t cheating. He never even talked to me about how he thought I was cheating he just did it...I don’t know what to do....I’m not even crying I just feel numb...

Just to justify his idea of not being affectionate is that we weren’t having sex multiple times a week. I’m a full time mom I’m in school I volunteer and work. He has also been really mean to me lately causing me not to want to be affectionate. I’ve talked to him about those things and he just shrugs it off. I make dinner an clean the house. I cuddle him at night and tell him I love him every morning. I suggest going on date nights and he says no. There was no reason for him to look somewhere else.