Welcome Amylou -
I too have to say, I am not impressed with your spouse, and I am more concerned that you feel snooping is bad.
Those with nothing to hide, Hide NOTHING!!!!
He is your Husband, you have every right in the world to look at his phone, FB, and everything else, and if he gets pissy it's because he is hiding more.
You do need to confront him on this, and probably need to get some MC sessions scheduled. There are definitely some communication issues going on, and the sooner the two of you work through that the better off you will be.
He knows he was being bad, he knows he was crossing a line, but the question is WHY was he even considering it? Why did he put out that vibe?
You need to really put his feet to the fire on this one.