I would simply tell DH, "You 'volunteered' us to host this event. This will cost approximately $$$. Here is our budget for the next few months. The only way we can afford this $$$ dinner is if we cut out this and that and this (preferably things that would affect him somehow, primarily entertainment/dining out). If you still think we "must" host this dinner, then we can save $$ by moving the dinner to (less expensive restaurant) but we'll still have to find the money in our budget." If he complains, point out that you're the one making the money, you have to make sure all bills are paid, because dinner out with your MIL and her relatives are lower on the list of priorities than say, rent, student loans, etc. "But we can put it on the credit card" Tell him point blank you are not going into debt to fund a dinner that you did not agree to with people you do not know and at a far more expensive restaurant than you would normally attend - AND your parents are excluded?
If he complains further, simply call up MIL and say "It appears there was some breakdown in communication, but I will not be attending this dinner." If he goes alone, fine, but make sure that money comes out of HIS pocket somehow - all of his 'fun money' for a few months if need be, etc. The consequence is his to bear for screwing this up if he insists on going and spending that money.
If you choose not to ruffle feathers and go ahead with the dinner - definitely scale down. "Sorry, we cannot afford $$$ restaurant. There's a lovely restaurant in an affordable price range at (location)." Then do go ahead and invite your parents, since they're paying for themselves (so cost is out of the equation) because it is now your dinner.
I honestly would make this a hill to die on personally - not just MIL's audacious assumptions but DH's "putting his foot down" and insisting that you pay for this dinner.