In this paper, the commonly used but idealistic formulation of quantized optical-phonon modes for a heterostructure system with only two heterojunctions (i.e., single quantum-well structures) is extended to the more realistic case of multiheterointerface structures. By applying the macroscopic dielectric continuum approach, dispersion relations and interaction Hamiltonians for interface-phonon modes are derived for a double-barrier structure and scattering rates based on these results are used to determine the range of practical validity of the idealistic model using interaction Hamiltonians appropriate for single quantum wells with infinite barrier widths. It is found that when the dimensions of the structures are larger than approximately 30 Å, this simplified description can be applied to multiheterointerface structures in general with reasonable accuracy.