I lately found out a friend was in a similar situation, prior to christmas her DH was texting/being texted by a woman and staying out at night... long story short, she was chasing him and nothing happened... my friend was soooo upset, she went into a depression over christmas and into january, she didn't tell me until it was all over... She eventually believed him that nothing happened, and most importantly, he has taken the steps to prove to her that its all above board... his behaviour has changed and he is putting more effort into her and their relationship...
One thing that is a really good sign is that she has invited your family over. I know that would be a daunting invitation but why would she say it if there is an affair going on?
i can understand how upset you would be over this, it was 8-10 weeks before my friend could tell me what was going on and I know for a fact that i am one of the very few that she would confide in.
I agree with AM, you need to talk to him, and he needs to take steps to restore yur faith what a horrible situation