I think jumping is not necessary, just check for available TU ~25-50% and "teleport" from one side of small fence to another side if there is free space.
I didn't mean literal jumping animation, that would be a bitch to draw for every armour ever... Well, I guess you could use the kneeling pose maybe...
In climbing up also check for available TU ~75-100%, another soldier nearby, free space on the next floor and "teleport"
I'm not a fan of "teleporting", it would look bad. X-Com has a nice way of visualizing things, so we shouldn't really add elements that are inferior in this regard.