Proper use of isometric tilemap

So I’m experimenting with 2D isometric tilesets / tilemaps but I don’t know what’s the proper use of them, as there is not much documentation.

I started grabbing the tileset from 28014-. The result looks good, but here comes my problem:

If I position the tile map perpendicular (as in it were an actual floor) to the paper character (who was an ortographic camera) the tile map looks bad, but I can use tilemap collisions.

If I position the tile map parallel (and behind) the paper characters it looks good but if I move the character on the Y axis it can get behind the tile map. Also, I can not use the tilemap collisions and I’d have to emulate them somehow.

So, how can I use the tile map and move in both the X and the Y axis?