By using direct numerical-solution techniques for the reflectance (R) and transmittance (T) equations of a multilayer structure, we have analyzed infrared R and T measurements on heavily doped p-type GaAs:C films grown by molecular beam epitaxy. The optical properties, for films with hole concentrations up to 1.4x10(20) cm(-3), were determined for photon energies from 0.07 to 0.6 eV, in which region plasmon (intraband) and intervalenceband contributions are in competition. Our results for the optical absorption coefficient resolve two separate peaks located (at high doping) at about 0.1 and 0.2 eV. By carrying out calculations of the intervalenceband (IVB) absorption processes for our dopings, we identify the peak near 0.2 eV with light-hole to heavy-hole IVB transitions, and we attribute the lower-energy peak to hole-plasmon excitations. Our experimental absorption spectra are very well described by a model combining the IVB contribution to the dielectric function with a plasmon contribution. The hole-plasmon parameters we obtain for highly doped p-GaAs yield an infrared mobility which (unlike the too-small IVB-entangled infrared mobility implied by the use of the usual effective-plasmon model) is in substantial agreement with the dc mobility. (C) 2002 American Institute of Physics.