Well, for starters, instead of Wife replying to all invitations issued to the couple jointly, Husband can step up and start fielding those, even if he does not want to go. Let him handle his own refusals that way. "I can't make it, but Wife can!" Of course Wife is cc'd on the reply, and I sure hope Wife is already cc'ing him on all the back and forth that managing his social life is creating.

I'm not saying he needs to get out more (Prudence's solution, although I think that's actually a good idea, because right now he is requiring everyone to work around him in a very privileged-male way). I'm saying he needs to own his choices and do the work to manage his social interactions.