Thanks again for all the suggestions. Cheshire, I'm very sorry for your loss.
When my mom was originally diagnosed, my dad thought that he'd sell the house right away, that it would be too painful to be there without her. Now, even though it hurts, he loves feeling her presence around him. Like I said before, every square inch of the house has my mom's touch. It was their dream house. There are a couple reasons, albeit not the most financially sound, that we'd like him to keep the house. First, it's a way for him to still feel close to my mom. It brings him comfort and that's a pretty high priority for us. Second, he has tons of support from the neighbors. They bring meals, offer support, and help out any way they can. He'd lose that if he moved to a new neighborhood. Third, my sister lives within walking distance and I'm about a 10 minute drive away (can you tell we're close?). Having him so close makes it easy for us to hang out over there so he's not alone, cook him meals when he isn't feeling up to it, and generally be there for him on a moment's notice. He gets a lot of comfort from being with the grandkids and wants to stay close to them. After my mom died, he said to me that the house he's in now feels like home and my mom made it that way. For the rest of his life, any other house will just be a house, not a home. He might change his mind in the future but for now I totally understand what he's saying.
The house is in a neighborhood that is still rapidly appreciating faster than surrounding areas. He'd be better off building equity in the house he has now than moving. He'd like to be able to stay in the house until he retires in about 11 years. Then he'll sell it and move into something smaller. He'd actaully love to buy my house to retire in. It's a 1600 square foot rambler on just under an acre. The area is a tiny pocket of semi-rural living within the city. It has a nice big garage where he could tinker with his toys (his favorite hobby). Our current next door neighbors are in their late 70s and will probably be ready to sell by the time my dad is nearing retirement. I would love to buy their house and sell my house to my dad. I know, it's a long shot but it sure would be nice.

Suggesting meeting with a financial planner is a great idea. How do I go about finding someone reputable? We do feel like we're in a time crunch. If he is going to stay in the house, it HAS to be refi'd soon because he can't cover that big of a mortgage on his own.