My ten cents - he is totally out of order. You need to sit him down and tell him you are not going to put up with it. Even if he is doing nothing wrong, he shouldnt be feesling guilty enough to have to hide it from you.
I agree with the majority of the girls here - and I think you need lots and lots of
Councelling is perhaps the best option - he needs to learn to be open about his feelings even if they are not want he wants to feel - you have a right to know about them and to deal with them together - there is no point in pretending!
My ex husband used to do the same - i know he never intended to meet these girls - but in the end we sat down and confronted the fact that he had a need to do these things in the first place - which was an indicator something was wrong in our relationship - something in fact, it turned out that he couldn't do for me which made him feel inadequate. Turned out I didn't love him and he sensed it and was insecure about that - not saying this is what your problem is at all! Could be a million things - just there is always an underlying reason.