So you have movement type 0 = walking 1 = flying 2 = sliding
Now 3 = Jumping
Jumping is flying for current turn only. Once you click end turn the unit falls down to the ground then next turn begins.
Jumping allows temporary 3d movement but unit cannot maintain flight during enemy turn.
Furthermore if a jumping unit is in the air with nothing solid underneath them they cannot use any attacks . A message "you cannot attack while in the air" will be shown. Or even "you cannot attack in mid air while jumping"
This is probably the simplest and most elegant way without having to create any special animations or code.
I was also thinking hoping over fences movement unrelated to the above or windows by temporarily switching over to kneel animation and moving the character up a bit faking a mid jump over medium sized obstacle.