You drop him like you would a hot potato. My soon to be ExAH has done this. He went as far as texting his niece by marriage (she was 19) and told her his off days and that i would not be at home and invited her over for a night of sex. When i confronted him, he told me someone hacked him! I said, that's pretty damn funny that someone would hack you and know EXACTLY what days you were off and when I'm at work!
This is an unhealthy marriage, drinking aside. If he's willing to sext women, he's willinbg to have sex with them.