In reply to a comment, I will describe how to apply the veneer paper to the MDF matrix. The veneer I have used, is called Microwood, which is a 0.1 mm veneer with paper backing.
Before the final full-surface bonding onto the MDF matrix, I did some pre-testing with the glue and the surface preparation of the MDF. To avoid paper curling after the adhesion, I used a solvent based all purpose adhesive (UHU black), which worked as expected. For testing purpose, the black laser cutting edge on the MDF surface was removed with sand paper:
The following image shows the veneer glued on the MDF sanded off (right) in comparison to the veneer glued on the more or less black MDF. For me, this difference was not enough to polish all the MDF parts and the final result proved me right.
Because of the paper backing, it is quite easy to apply the veneer and there is no problem with dissolving, although the veneer was rolled up when it arrived.
If you have any questions, leave a comment.