Hi there. Sounds alot like my WH. Only his cyber cheating escalated. He's heavy into porn, and cyber sex - some very unsavory business. In addition he has added over the last 20 years of marriage, multiple prostitutes, and a few COW, that I know about. I have confronted him multiple times over the years. I just found this place this month. I have come to realize he does not care about anything or anyone else, but himself and his perverted desires. Even if he does "little things" around the house, its because he wants bragging rights - "Well I put that bowl in the dishwasher." "I picked up that piece of dog food..." Some WH don't get it. They are not wired for it.
See if he is willing to REALLY take responsibility - cyber cheating is still cheating, and can escalate into more if left unchecked... (I live with the poster child on that one.) It is possible he already has, and you just haven't seen proof yet.
He has to be willing to be a full partner in your marriage and children's lives.
I wish you luck and you have found a great place to get advice and strength. I certainly have.
(((hugs))) and strength to you