Yes. "Above" and "over" mean the same thing in this sentence. I'd like your sentence more if you used "heads" instead of "head". You and the other people who live there don't really share one head, do you?
I agree with Suzi. Yes, over and above can mean the same thing, and when talking about roofs, they do mean the same thing. But for me the idiom is always "roof over our heads," never "above our heads."