According to my company(XJ) TSA (AKA the smurfs) do not allow riding in the jumpseat in either direction. We can't even ride on our own js international much less anyone else.
Hey Avroman, according to the FOM you are 100% correct. However I have e-mailed our Jumpseat rep and he claims XJ pilots are allowed to sit in the cockpit jumpseat on international flights as long as its a XJ operated flight. He then tried to get this ability revised in the FOM and I haven't heard back.
This is similar to other airlines. I know Expressjet and Compass are the same.