Abstract: An assembly between a metal piece and a ceramic material piece made of SiC and/or C based ceramic material. The assembly includes a stack structure including the following elements assembled together in pairs in this order, by brazing: the metal piece; a first intermediate piece; a second intermediate piece; and the ceramic material piece. The second intermediate piece is made of another ceramic material, that is chemically less reactive relative to metals than are SiC or C, and that presents a coefficient of expansion smaller than that of the material constituting the metal piece. The first intermediate piece is made of metal and can deform to compensate for expansion difference between the metal piece and the second intermediate piece. The assembly can be used in a turbomachine.