I figured out how to tilemap easily enough but I can't seem to get objects to overlap properly.
Note, I have reviewed many articles and none of them seem to describe in detail how to accomplish my task.
What I have...
I've provided a picture demonstrating my problem. The bear rug on the right is placed on a layer(objects) separate from the background(terrain). You will notice that the transparent parts are cutting through the terrain layer rather than actually being transparent.
The bear rug on the left is the desired result.
Creating two tilemaps does the trick, kind of. You have to change the zOrder of each tileset to the appropriate setting. However, in the free version you cannot do this. Excellent.