I have been in a relationship exactly like this. I was with first "D"H for 20 years. Over that time, there had been multiple incidents that were dubious, but could be explained away. Then one day, his best friend told me everything, about how he had been chasing multiple women for years. It was horrifying.
Once my eyes had been opened, it became more obvious when we were out together. Leaving his hand on women's knees for far too long, disappearing in night clubs with colleagues, letting women sit on his lap. Then it progressed to him staying out all night at a female colleagues flat, when the arrangement had been to stay with a male colleague. This was despite several warnings from me, about me leaving him if he didn't stop.
I can 100% imagine the scenario where he would do what your DH did. And the minimising was also the same. It drives you mad. I hung on in there for 4 years, hoping he would stop, but he just never did, so I finally left him. He was completely amazed that I would leave. Even after all the warnings. That's how arrogant he was.
I am now married to someone else, and this scenario seems so far fetched you may as well be talking about aliens. I think unless someone has been married to one of these men, it's so hard to comprehend.
I know you won't leave him immediately - I certainly didn't - but be on guard. I would try your absolute hardest to get access to that phone. My H got almighty pissed one night and passed out. I got in to his phone, and there was evidence of an affair that he had been having - with my very best friend. So that was nice. They both denied it, but I had all of the evidence.
Let me say also, if you do break up, there is life after all of this. I actually enjoyed being free and dating for a while. It was liberating and exciting, after being stuck with him for 20 years.