Acoustic-phonon transmission and reflection amplitudes are evaluated for semiconductor superlattices. The calculation is based on a finite application of the transfer-matrix method, which permits one to take into account both the crystal anisotropy and the coupling between excited modes of different polarizations. This method is applied to multiple-layered structures, thus allowing the study of more realistic systems, such as superlattices with disordered interfaces. The angular dependence of edge and anticrossing gaps is analyzed. The method has proved successful in explaining recently available experimental data on amorphous semiconductor superlattices.