An assembly for wall covering, includes a fastening structure provided with a body, an anchoring face, recesses having an insertion portion, two facing parallel upper reception portions, two facing parallel lower reception portions, and two support blocks, each block bordered in part by one of the upper and lower edges of the insertion portion and by the upper and lower reception portions. A fastening interface is configured to be attached to a covering element and to be mounted on the structure, which interface includes three branches, two of these branches projecting from a first branch configured to be inserted into the insertion portion then slid against a face of the body along a block and with the other branches being configured to be received in the upper or lower portions.