If those are the elements you're looking for in your game, House on Haunted Hill will be pretty much up your alley
I assume your talking about Betrayal at House on Hill. I can't find any reference to a House on Haunted Hill board game. Unfortunately it is out of print but you can find it in a few places. I don't quite like the style of it (a little bit comic for my taste) and I want a bit more in-depth and integrated story and apparently it also has a few balance issues. I might order a copy anyway as it still sounds like it could be fun to play.