Do you have enough equity in your "face up" house to make up the difference between the probable selling price and the mortgage amount of your "underwater" house? If so, you will need to take the "face up" house off the market and take out a equity loan, aka, 2nd mortgage (or in your case 3rd). Keep that money in reserve, then when you go to sell the "underwater" house you will have the cash that you need to bring to closing. The fact is that if you sell for less than what you owe you will either need to bring cash to closing, which can come from your savings account or negotiate a short sale.

Is it possible to rent out the "underwater" house and cover your mortgage (or close to it) with the rent?

I don't see being upside down on a home as this horrible thing, so long as you can make the payments, or have rents to cover them. Eventually, either through paying down the mortgage or market appreciation, you will likely have an equity position in both homes again. You may just have to ride this one out.

The only time being upside down is a real problem is when you have to sell.

Sell the face up house. Take the equity and pay off or pay down the 2nd mortgaqge on the upside down house. This is the responsible thing to do.