Yes, he is. It's why you had sex in a vehicle at 4am on the side of the road as opposed to one your houses.
Kit, you're right, it's your life to do what you want with it. So do you.
But, if you think you're going to come here and get buy-in or convince us (maybe to convince yourself?) that your husband has changed his cheating and lying ways, I just don't think anyone here will get onboard with that.
The honesty here is brutal, but it is honest. And I don't think you would want us to blow smoke up your a$$, right?
Again, your life, your decision. But I think you are setting yourself up for another fall.