If you are on a team, invisible, certain entities do not render through the invisible player. Not having much time at the moment, I was able to compile a few of these entities that do not render through the player. These include:
Armor Stands
Chests
Chests, Furnaces, and Command Blocks in minecarts
Cows
Creepers
Dolphins
Donkeys
Ender Chests
Items (on ground and in hand)
Item Frames
Trapped Chests

Picture below is an example