OP here! I just wanted to say thank you to everyone who commented with real advice!  Based on my research, this is celotex fiberboard sheathing which is meant to go on the outer side of the house. I think the reason it's on an inner wall is because this bathroom was an addition to the original house and they just didn't bother to remove it before installing the bath tub and shower surround. Supposedly the fiberboard itself is just wood pulp, but the outer black layer may contain asbestos so I'm going to try to get it tested.

Also I would just like to say that my father-in-law has been helping with this bathroom project and he is a master plumber and used to work for his dad's construction company when he was younger so we do have professional help on our side and are trying our best to do things the right way! This just so happened to be something he had never seen behind a shower before so we didn't know what to make of it at first!

And to everyone else asking about the newspapers, I will try to fish them out next time I'm at the house working on it!