Gmod would be PERFECT for what we want to do. We play L4D2 which is a lot of fun with the splitscreen mod, but that's co-op only and doesn't fully satiate what I'm trying to accomplish.
His favorite was Halo and while I don't need anything similar to Halo, it would be great to have an FPS where the two of us can just shoot at each other in a map of our choosing.
Now that I've switched fully to PC, my dad and I don't really have any FPS games that we can play together on the big screen.