Anomalous mode-converted transmission of phonons is studied based on the new formulas for the transmitted amplitudes of phonons propagating oblique to the layer interfaces of superlattices. A transfer matrix which well describes the transmission of the coupled longitudinal and transverse phonons in an isotropic model is introduced. With the use of this transfer matrix we can derive finite difference equations which govern the transmitted amplitudes of both the longitudinal and transverse phonons. These equations can be solved exactly for periodic superlattices and approximately for certain aperiodic superlattices. The results are applied to the study of the unusual intermode oscillations in phonon transmission in both periodic superlattices and aperiodic superlattices with variable thickness of bilayers.