It can be tricky, landing that monstrosity. Even stones and small plants can interfere with landings. Try finding a clear patch of road. And remember to think 3D. Where it is in the air on screen is not where it will be when you land...

I am having the same problem, I can't "exit" the carpet. I can land it but that is all. If I enter combat mode, I will stand but can't walk of the carpet. Is there a key or something that I am supposed to press? I have been trying everything I can think of for the last 30 minutes with no luck.

EDIT: I just was able to figure it out. I went into an open area, clicked on an empty seat and it landed. I feel foolish now.

Right, you have to "use" the carpet, not the passengers or ground.

The other challenge, as noted above, is that the carpet will attempt to land on whatever is at the center of the screen, and that isn't always easy to gauge.