But first, definitely figure out if keeping the house IS the right thing for you. It doesn't sound like you have much equity in it if you are going to have to pay PMI. One of the biggest financial mistakes women make is to hold onto the family home they can't afford in a divorce, in an attempt to keep things "normal" for the kids.
That being said, the market IS low. If the payments would be less than rent AND you expect to have enough money for upkeep on the house, AND you can refi, AND your H agrees to a divorce agreement that doesn't require you to refinance the house again (but I can't imagine that an attorney wouldn't advise him against agreeing to that).....
Ask yourself - would you buy this house today, at this price? Or if you end up divorced, would you be considering moving closer to family or to a less expensive neighborhood?
You should ask yourself all these questions before you refi.
As for what your H gets out of this: he may get to look like the "good guy". He may be interested in maintaining the family home for the kids' sake. He may be trying to avoid having a foreclosure on his record (if the house is underwater - is it?).
Also - if you do refi - don't do anything other than a fixed rate. Try not to extend the length of your loan by too much (i.e., if you have 15 years left on your current mortgage, don't refi to a 30 year). And as for the PMI - you may not be able to get rid of the PMI until your mortgage is paid down to a certain percent (70 or 80%)regardless of what the market value is - read your paperwork carefully.
