An acoustic resonator assembly includes a layer of high-acoustic-impedance material and a layer of low-acoustic-impedance material made of a low-electrical-permittivity material. This assembly may support the resonator over an interconnect layer or act as a decoupling assembly between two active elements of the resonator. The assembly may alternatively include three low-acoustic impedance layers. Alternatively, the assembly may include three acoustic impedance layers wherein two of the layers are low acoustic impedance layers and the third layer has a higher acoustic impedance than the first two or alternatively is a high-acoustic impedance layer.