NauticalMile's answer is great (and bonus points for the killer animated diagrams). To give an alternate suggestion that doesn't suffer from the same problems (the wheel collision stopping you from moving past objects that a floating body should be able to traverse effortlessly, I suggest modelling something more closely matched to the reality of your situation. I.e. don't use rigid body collision and springs.
Model your character as a rigid box as normal, but every update do a raycast directly downwards (in the direction of your jet thrust) and measure the distance from the character to the nearest collidable object. Then, apply an upward impulse to your character's body, inversely proportional to the distance from the ground. So the closer you are to the ground, the larger the impulse. That can be a linear proportion, or an exponential proportion, but you don't want it to be too large (i.e. shooting off into the sky) so you'll want to damp it beyond a certain range. But basically it should achieve equilibrium against the effects of gravity, to give the effect of a spring - the closer you get to the ground, the more energy the spring imparts, the further away the less it boosts you. Combined with a damping factor on the motion, you should achieve a balance point some height off the 'ground'.
NB: this force should be constrained to only act vertically on your body, otherwise you start getting into real-world issues where your character is unstable and wants to lurch forwards or backwards depending on what's underneath or what angle the character is at.
Jumping is then simply adding an extra vertical factor to that force - you can't jump infinitely high, but it does have the extra nuance that if you time the jump right (say just after dropping down from a height), you can get extra height on the jump by taking advantage of the bounce effect.
This should have the effect of allowing smooth motion over small obstacles without taking anything away from your horizontal velocity. As the obstacle comes under the jet raycast, the character will shift upwards, but not slow down at all.
Actually, a single raycast may be unstable, especially if you're moving over rough terrain. I'd perhaps do two or three raycasts and take an average of the distance; weighting it if you want to maybe, or discarding measurements outwith a certain deviation from the average. What you're don't want a case where the character moves over a very slim gap in an otherwise flat surface in the world and drops downward sharply because the ray happened to pierce right into that gap.