Double-sided DVD movie won't play

I recently bought a single DVD that has two movies on it, one on Side A, and one on Side B. I was going to watch them on the Mac. When I put the DVD in, it played the movie on Side A with no problem. When I flipped the DVD over to watch the second movie, the computer ejected it. I've tried it several more times, it reads one side, but doesn't even recognize the other side. I don't get any errors, nothing--you can hear the drive trying to read it, then after a few seconds, the computer ejects it.

I've tried the DVD in my regular DVD player and it played both sides. I also tried it on a friends desktop computer (running windows) and it recognized both sides.

I've got all the latest software and firmware updates. I can't figure out why it plays one side, but not the other?? This is just a regular DVD movie, nothing weird. Any suggestions would be appreciated!!