Minbari ships can fly in atmosphere, there was a CGI sequence somewhere where we see a bunch of Nials flying in Minbar atmosphere. Even though Sharlin is a big ship, technically it should be atmosphere capable. Also, in the Legend of the Rangers movie we see the big EA-Minbari hybrid cruiser taking off from ground, which suggests that Minbari engine tech is advanced enough to make even a Sharlin atm. capable. Vorchan, Primus and Sentri probably are technically atm. capable as well. Rutarian probably uses same engine tech as Sentri which would make it atm. capable. Narns don't have gravimetric drive tech until ISA so their pre-ISA designs probably are not atm. capable. Drakh and Vorlon ships definitely are atm. capable. If we take the books into account as well, then it is clear that all military Minbari and Centauri ships are atm. capable.
Now Drazi, that's the most difficult topic so far. Marcus escaping in a Sun- or Firehawk from the planet suggests that Fire-/SunHawks could be atm. capable. Drazi engine tech is quite unique looking anyway, while not gravimetric could possibly allow atm. capability. While Sun-/Firehawks probably are atm. capable, Sky Serpents may not be which is supported by the fact that Marcus' Sky Serpent was attached to a Fire-/Sunhawk and then launched after they had cleared the planet's vicinity.