The infrared dielectric function of thick GaAs1−xPx alloy layers grown on (001) GaAs substrates by hydride vapor phase epitaxy was investigated in the reststrahlen region using Fourier-transform infrared ellipsometry. The spectra are influenced by the Berreman artifact at the longitudinal optical phonon frequency of the GaAs substrate and by interference fringes due to the finite layer thickness. The ellipsometric angles were analyzed to determine the dielectric function of the alloy layer. Two-mode behavior, including strong GaAs-like and GaP-like optical phonons, was observed, confirming the results of Verleur and Barker [Phys. Rev. 149, 715 (1966)]. Due to the increased sensitivity of ellipsometry in the reststrahlen region, several weak phonon features could also be seen. The lattice absorption peaks are asymmetric and show side bands at the lower and higher frequencies. A single additional peak, as suggested by the percolation model, does not describe the spectra. The cluster model proposed by Verleur and Barker is a better fit to the data. Due to the broadening of the phonon absorption peaks, the authors were unable to find a unique decomposition into multiple components.