You know, this isn't just going to be an issue between two students; this continues to be an issue in the professional world, the problem is you don't have a lot of experience behind you to come up with great solutions to the issue at hand.
I think someone, and this is probably you, needs to point out the elephant in the room, and come together and have a conversation - perhaps accenting the issue of communication, and wanting to improve that - both ways - and find a way you can truly be working together as a team. My history in problem solving would be to keep the issues clean and separate, not about you or the other person. "I wish we were better at communicating" is better then "You need to stop hording information." Offering creative, positive, upbeat solutions that you can implement . . . may help the situation.
But, I am not Polyana-ish enough to rule out the two of you might be oil and water and there maybe no way to make this idea - you need to figure out a way to work together - but you may never like it. As the assistant, you need to accommodate the other person's style and way of working. Check the passive aggressive crap at the door, and genuinely support them. If he is not giving you the information you need to do the job, don't throw him under the bus - all you need to do is say "I am sorry, I thought I had all the notes about this set piece, apparently there are somethings they may not have gotten to me." This happens all the time.
I wish you luck, and keep us up to date.