The AirTrain is 98% above ground, but does enter tunnels a couple of times to avoid roadways. But, as best I know, does not go underneath a terminal or anything like that.
Originally Posted by
SDF_Traveler
Edit to add: Tram is above ground - doesn't really go into any terminal, but is connected by above roadway bridges, including the "International Arrivals Building" - IAB. Just about every terminal at JFK is an international arrivals terminal with an FIS. The IAB is also known as T4, will soon be vacated primarily for DL, as I understand it.
--Jon