Maybe it was not available yet when this question was first answered, but to be clear, you can change the z_index of individual tiles in an atlas or autotile. There is a tab for z_index on the same menu where you can select a region of tiles, set bitmasks, collisions, etc for a tilemap. You can set the bottom tiles of an object to have a different z_index for example.
However, if you are trying to have a player be able to go behind and in front of objects in top down 2D world, it may be better to go with a solution like LuminousSilver mentioned. I would recommend creating each object as a sprite and make all the sprites the child of some node. Add all the sprites to a group. Then you can attach a script to the parent node to call all the nodes in the group and set the z_index equal to their y position. For example, I put all my building sprites in the group "Buildings". I add the following code:
To the player:
z_index = position.y
To the parent node of the building sprites:
var nodes = get_tree().get_nodes_in_group("Buildings")
for node in nodes:
node.z_index = node.position.y