First of all let me say you are very brave for dealing with this.
Perhaps the others are right in their "validate him" "thank him for his honesty" and "cut him some slack advice." I have no idea, this is way beyond my experience or expertise. My initial feeling is that that kind of advice implicates that you can help him--I don't think you can. It seems to me he expects you to just accept his apology and despite the fact he's a repeat offender, not have any trust issues. The only way he is going to "get better" is if he makes a huge effort to get help and it will take time. In that time, I think you need to get on with your life.
My gut feeling is that is very screwed up, more than the average DBer can know how to handle. He is a liar, that you know. He is a probably a sex addict and God knows what other kind of addict. He has cheated not once, not twice, but how many times? That you know of? He is humble and crying one day, abusive and brash the next. He's not right in the head and you cannot help him with that.
I'm so sorry that you have to deal with this. I will not give any advice other than to say both of you need to be in therapy--individually and perhaps even together. Like cancer or diabetes this will not cure itself--you both need to get help.
