Oh, that's a tough one! BUT in the financial situation that we're in at the moment, I would probably shove my husband out the door with a big kiss!
How often would he be home? My husband, years ago before we had kids, worked for Schlumberger (oil well testing). He was "on 6 days, off 3". The schedule was weird because occasionally he was actually gone for up to 6 days. Other times he just worked during the day during those "on" times and was on call during the night. The money was good (for us back in those times) and since we didn't have kids yet, it was no big deal.
Like I said, that's a tough decision but financially, it would put a huge dent in those bills. Would it be easy enough for him to return to his old job after a while or find a new one closer? Maybe you could set a time limit on it and everyone just buckle down and "sacrifice"??
Good luck!!