Ahhhh... I've had the same problem before, just not with the 'falling to your death after crossing the adjoin' problem.
Well, go into JED (if you're using JKEdit, then I can't help u, lol), and go to the adjoin. First make sure the sectors are actually adjoined and don't just somehow overlap. Then go to the 3D preview and check to see if there are and 'fragments' of material in the way. I don't think you did the adjoin correctly maybe? Or, perhaps, the floor of your adjoin may not have a floor flag assigned to it.
I don't know. What I said is probably unreliable. When I had my problem, I think I had to restart working on my level, but I was only working on the early stages of it.
(You could eventually cross my original adjoin with some work, and even though I had the floor on the other set as floor, you would 'sinkin' and wouldn't be able to get out of the room without considerable effort. Once you managed to cross the adjoin, you wouldn't be able to move around the room inside, either.)