A composite structure for an acoustic wave device comprising a heterostructure includes: a useful layer of piezoelectric material, having a first face and a second face, the first face being arranged at a first bonding interface on a support substrate having a coefficient of thermal expansion less than that of the useful layer, wherein the composite structure further comprises a functional layer, an entire surface of which is arranged at a second bonding interface on the second face of the useful layer and having a coefficient of thermal expansion less than that of the useful layer. Methods are used for producing such a composite structure.