My ex was like this. The "little jabs" are expressions of hostility. The accusations of infidelity were expressions of his inability to trust another human being. Interestingly, I never cheated on him, and we've been divorced 3 years and I have yet to begin dating. (There you see my 20-years-with-an-alcoholic trust issues on display.) He, however, was on match dot com right away and had a new steady GF about a week after he moved out from our family home.
I lived with this type of hostility and distrust for decades - there is nothing more destructive to intimacy. Wish I could give you hope that he will come out a new man.