I didn't see the screenshots, but your description of what's going on is enough. If you have to ask yourself (and others) if this kind of thing is okay, perhaps try to imagine a friend or sister was asking you the same thing - her husband is texting/emailing/calling girls, hiding it, becoming defensive, protesting loudly that she is more than enough for him ... what do you tell your friend?
It's possible that he honestly can't see a problem with his behaviour, and maybe - just maybe - it really is as innocent as he says. But it's a problem for you, which makes it a real problem regardless. Take care of yourself (and, I hate to bring this up, but perhaps a test or two at the doctor's? Just to be sure he's not been bringing anything home that he shouldn't?)