Still looking into the jumping, Dark Side (1988) had a jetpack so there's that kind of vertical movement in the game, but it's not the same thing.
As for controllable vehicles, there's The Colony (1987 or 1988) for the Macintosh. It's one of the earliest examples of realtime first person adventure/puzzle game with 3D graphics. The interesting thing is that there's a forklift vehicle you can enter and drive: https://www.youtube.com/watch?v=i1XENlUUOhA&feature=player_detailpage#t=362
Now that I think about it, Mercenary (1985) had the drivable land and air vehicles in a realtime 3D environment, just not with filled, shaded polygons.
Btw, The Colony might have a lot of firsts like storytelling told through logs, it was very exploration oriented, it had a main mission (power up your crashed ship and stop an evil alien race) but it also had completely optional sidequests, realtime top view mini map and maybe has the first flushable toilet in a first person game. The tvtropes entry has a lot of details about possible firsts, like having a ripped sample from 2001: A Space Odyssey or having a holiday mode (On December 25, the potted plants become Christmas trees) .
Excellent. Updating the jumping entry, at least.
Edit: also, Dark Side (Atari ST, 1988) appears to have also had vertical free-looking before Ultima Underworld.