Tim;
I work for Verizon, and we're going through the same issues. We're had over 10 RIFs ("Reduction In Force", or mass firings, for those lucky enough to not know CorporateSpeak) over the past six years, and two mass forced relocations similar to what's happening to you. So far I've been spared, but I never stop looking over my shoulder. I will say that of my friends who have been affected, most of them have ended up in at least as good a situation as before, if not better.
This is a great market to buy a home, not so good for selling. Military areas tend to be more stable than others pricewise. If you can pull it off, your best bet is to rent your old place out for enough to pay mortgage, taxes and upkeep, and rent or, if possible, buy at your new location while the market's down. If you're renting out your old place for enough rent, that neutralizes your outflow, hopefully by enough to get a loan for the new place.