The thonet grid seen in the image is a normal map with an alpha (possible in blender 2.76, but not later I think). the mesh for the thonet is included in the last layer - I didn't succed to make it completely tileable, though
The alpha in the normal map works fine in Blender 2.78, the problem is there's a solid door behind the grid.
Maybe cut some holes in TableDoorLeft and TableDoorRight?
ah. yes. Thank you for the remark. it's a missunderstanding, though. the thonet here is not supposed to go through the doors (but maybe that would be interesting). But anyway: the cylces-baked normalmap (2.76) for the thonet itself has an alpha-channel. that I'm using in the node-setup for the thonet-plane. When I tried to do the bake with my 2nd blender-installation (2.77a) I got an normalmap without alpha. It puzzled me so I looked it up and found some discussion of the "feature-change" here https://developer.blender.org/T48948.
Okay, I see what you mean about Alpha in Normal Maps not being possible past 2.76 (I did not know this).
But my point still stands ... the thonet (I think we would call this 'wicker' in English) mesh should have holes in it. It does, but instead of showing the inside of the sideboard they just show the doors underneath the thonet grid(s). Hence my suggestion to cut some holes in these doors.
Cute art very nice thanks for the upload, happy blending.