Did you end up confronting him?
I can relate to this situation with my own SO, only it has been time and time again that I have caught him in his porn addiction because he let's it interfere with day to day life. I always jump the gun though and I always get confrontational which is a poor strategy, honestly. It always ends in us fighting it out, having our words out at each other and then me forgiving him under certain conditions and agreements which may or may not be followed through.

He had an emotional affair mixed up in all this. This is a grey area, however. He had the intent of getting us into some "threesome" or so he claims but it was entirely behind my back when it should have been brought up with me before he even messaged her. Also, the way he spoke to her and the things he said were not ok for a man who is in a monogamous relationship to say. I had a dislike for this woman and when he found out his threesome was not going to happen he continued to speak with her until caught- long winded, but just to clarify. It is similar of your own partner was looking for a third as well? My SO never touched her though. That is the only reason we remain together.

Trust is a hard thing go regain once it has been shattered. Some times it is even irrepairable. I might suggest though going into the app to see if it is collecting dust or if he has indeed been active on it and go from there. Or even check from your own end if you still have an account if he has been active?

I do not think that going onto a significant others phone is 'cheating'. If someone has nothing to hide and they are faithful, themselves, then there would be no problem.
Understandably he will probably grow defensive when he finds out that you snooped and will try to turn it on to you. I guess it is going to be a discussion you will have to have.

It has gotten to the point in our own series of ultimatums that my SO is no longer allowed to have a password I do not know. He did this freely in an attempt to regain my trust. It is our compromise. He has my passwords, too. He always does though, I am lame and never change them.

Anyways, I hope you will find an amiable solution or compromise with your own husband. I know it is a sickening feeling, stumbling across something like this.
Hugs, and good luck!