A one-dimensional local-mode model is developed to describe phonons propagating normal to the layers of (GaAs)n1/(AlAs)n2 superlattices, in which the effects of broadening of the interfaces can be quantitatively described. The model is applied to the analysis of Raman scattering and far-infrared (FIR) measurements on short-period superlattices, n1=n2=2,3,..., 8, and is shown to give a good description of data in both the GaAs and AlAs optic-phonon regions using an interface width parameter W of 1.4 lattice units. The model also describes the intensities of Raman-scattering modes, FIR dielectric scattering strengths, and linewidths. The analysis demonstrates that the effects of interface broadening must be included in an accurate description of phonons in short-period superlattices, and gives a quantitative assessment of interface quality that is in agreement with x-ray measurements. © 1992 The American Physical Society.