Personally, I don't think you can ignore things. He's definitely hiding something if he's quickly closing browser windows when you approach him. You say you've already established that he's going to online dating sites (guess he doesn't know how to clear his browser history), and that right there is a HUGE betrayal of you and your marriage.

What he is doing is a form of emotional infidelity. And it isn't that big a leap to go from that to real physical infidelity...

I would recommend that you see a counselor (by yourself initially) to plan out how to approach him to talk about your concerns, and to help YOU be clear about what your boundaries are (maybe you are okay with him chatting with women, maybe you're not, maybe this is a deal breaker for you if it continues, maybe you can't trust him any longer and want access to his email so you can check on his behavior, etc.).
Hopefully he will be willing to go with you after a few solo visits because it sounds like there are some issues that need discussed.
Good luck!