If you want and can afford the house, and if it's underwater so there would be a loss if it sold, then keep the house. (Don't keep it if it's a bad investment however). You will need to be able to refinance it in your name only eventually and take her off the mortgage. If you are financially able to do that, then yes, keep the house.
Now, if she is in the same financial position and would be able to keep the house yourself you might have a fight on your hands over it, but doesn't sound like she wants that.
I agree with others that you should consult an attorney if you haven't already. You need to get a clear idea of what you financial picture might look like after divorce, what your rights are, and how you might negotiate with her once the time comes. You also can get some information from them about how to protect your assets. Until you have some formal paperwork, as long as she's living in the house, I think any new debts she incurs become joint debts in most places.
My mantra would be - "You know I don't want a divorce but I won't stand in your way if you feel you have to leave".
