Let's Talk About Wallpaper

The only 2 rooms in our house that still need to be painted are the guest room & our bedroom. The guest room has 1 wall that is wallpapered, including a border. We assumed we'd have to strip the wallpaper off before painting. Not a big deal. Now our bedroom, that's a different story. First of all, it's painted this heinous shade of dark green. It's bad, but to make matters worse, we've recently discovered that underneath that horrible green is yet more wallpaper, presumably covering the entire room.

So here's my question, do we strip the wallpaper under the paint or just paint over it all as is? John is pretty anti-paint-over-it-as-is & wants to spend the time stripping the painted over wallpaper. I have zero experience in this arena. Have any of you ever had to strip wallpaper that's been painted over? Suggestions? Comments?

Super Fudge