I have soo many questions that I would want to ask him... I'm a question asker (drives my husband nuts because it forces him to address things he would rather ignore, but it's effective).
When he says he thinks the conversation about exchange students is pointless, I would want to know what topic of conversation he would find interesting.
If he always insists on "his" way - with television shows, activities, etc. or simply doesn't participate if he doesn't have "his" way - I would ask him when it would be "my" turn to have my way and get to spend some time with him. ESPECIALLY if I supported him during his activies.
Even without an event to discuss, I might bring up a conversation with him and ask him why it seems he's not interested in spending time with me.
I would ask him why he thinks it's okay to laugh at me and my ideas.
In fact, I might flat out ask him (if you're prepared for it) if he would rather not be in the marriage or family any longer.
Your comment about how, at the beginning, he asked for assistance in changing his ways, indicates to me that you may have started taking liberties with that opening and use it as a way to constantly criticize or critique even when he wasn't interested in changing.
If your husband feels like, over the years, he can't state something he feels/believes without you coming back at him with why it's wrong or even a minor correction, I don't blame him for checking out. That may not be the case, but it was in my marriage.
IF what I said above is even partially true (which I admit it may not be), then when your daughters were born, it may have gotten worse. A lot of women have a hard time "letting go" of the care of their children and are constantly telling their husbands that they're not doing X, Y, and Z right with the babies.
If I was in the situation your husband is in (based on my speculation), I would do what my therapist told me to do when I was going through treatment for depression and I would only do what made me happy. If I didn't like the conversation turning to how I was always wrong, I'd stop the conversation when it reached that point. If I didn't enjoy the activities with your friends, I wouldn't go.
I'm really not trying to blame you, as I only have this little window into your marriage - but to me, it sounds like he's tired of trying. He's tired of "deep" conversations, he's tired to being made to feel guilty that he's not generous enough with his time or money, and in some ways, it sounds like he doesn't feel "good enough." If your family is so altruistic, he may feel like he's being looked down on for not being that way (which is probably not true) and that may be why he doesn't want to visit your family.
I know this was long - but my best suggestions are to quit bugging him about his feelings/beliefs/choices and just go and do and be happy (bugging is a strong word - I'm not really trying to suggest you're always nagging him), and to also question question question to try to get to the underlying issues.