2.5D Platformer Camera follow character Y axis but not for every jump?

That's one is easy. Don't update Y position of camera all the time, update it only when player's on ground. In pseudocode:

 //updating position
 
 Vector3 pos = new Vector3(); 
 pos.x = player.transform.position.x; //'player' is public GameObject variable
 if (onGround){
   pos.y = player.transform.position.y; //'player' is public GameObject variable
 } else {
   pos.y = t$$anonymous$$s.transform.position.y;
 }
   pos.z = t$$anonymous$$s.transform.position.z;
 t$$anonymous$$s.transform.position = pos;

But you need to be aware that t$$anonymous$$s kind of scrolling is annoying from player's perspective and can be major annoyance, especially in shooting games (you won't see where you're jumping until you land).