Transit at Beijing airport to catch a connecting flight

There's no need for a permit if you do not clear immigration and customs. Normally, if you are arriving and departing from the same terminal, you will only need to clear transit security providing that your luggage is tagged to your final destination and your onward boarding pass has been issued.

Thank you John!
But my luggage won't be tagged to my final destination, as I got 2 separate flights from different airlines. That's why my concern. I'll be collecting luggage and checking in, and at some point going through customs. I will have to apply for a visa exemption? Thanks!

In that case, yes, you have to fill out a form plus provide a landing card and ticket receipt. Also be sure to leave at least 3 hours if you are switching terminals as new regulations require you to have your fingerprints taken on a machine before seeing an officer and that could take a long time. It will also take up to 40 minutes to get from T2 to T3 and vice versa.