For domestic US mail, it has been my understanding that after 9/11 only standard first class letters with a low weight (i.e. 1 oz) can be transported on commercial passenger aircraft.

Everything else is either transported by ground or on cargo aircraft. USPS has a huge contract with FedEx and a smaller contact with UPS.

For mail going overseas, I do believe this is where packages can actually be placed on commercial passenger aircraft. I believe such packages must be dropped off at the USPS counter and I think there are stricter rules (for international packages) about the application of self-postage. Not 100% sure on the latter.

This was my understanding as of a few years ago. It is possible things may have changed but I do know a large percentage of PriorityMail packages and most Express (next day air USPS) is transported by FedEx cargo aircraft.

I know both FedEx and UPS also contract some of their flying out to other cargo carriers, especially this time of year when they need the added capacity. Also contracted out is the "regional" flying with prop aircraft into the smaller markets and FWIW. I've also seen UPS contact with air carriers as well in "regional" markets (i.e. carriers like QX). I once met the UPS driver at a regional airport to get an urgent package that had been delayed -- This was pre 9/11, but I learned it was coming in on a Horizon Air flight from the local UPS office in a small city and met the UPS driver at baggage claim. Should have seen the look on his face, lol.

It wouldn't surprise me if there have been other changes in what commercial aircraft can carry. I've been on mainline flights like AA DFW-LAX and have seen big sacks of DHL packages/letters come out on the baggage claim with a DHL employee pulling it off -- the sacks were labeled with air carrier routing tags like you see on luggage "AA XXX -> DFW / AA XXX -> LAX".

I really question what types of cargo are placed on pax aircraft unscreened.

Speaking aircraft, does the US Postal Service operate any aircraft these days?