My husband has struggled over the years with one addiction after another, and that included sex addiction. It was thrilling to him to have a secret life that included cheating on me. Those women did not criticize him. Those women mostly did not complain if he failed to keep promises. He was big and strong and handsome. Translation: He was generous, and what they wanted was money and gifts.
An ‘affair’ may not be the same thing. However, I first found out my husband was having an ‘affair’, and it was actually one after another after another… I believe there is a connection between ADD and addiction. What you are seeing now may not be the whole story.
I agree your husband should not blame the ‘affair’ on impulses. He made a choice, and he can choose differently. For me, the critical thing was to get support to ‘stay in reality’, not be fooled by his stories, promises, lies. We both changed. We stayed together. It is taking years to restore trust, and I still have trust issues with him.
All the best,