Infrared reflectivity measurements (200-5000 cm(-1)) and transmittance measurements (500-5000 cm(-1)) have been carried out on heavily-doped GaAs:C films grown by molecular-beam epitaxy. With increasing carbon concentration, a broad reflectivity minimum develops in the 1000-3000 cm(-1) region and the one-phonon band near 270 cm(-1) rides on a progressively increasing high-reflectivity background, An effective; plasmon/one-phonon dielectric function with only two free parameters (plasma frequency omega(p) and damping constant gamma) gives a good description of the main features of both the reflectivity and transmittance spectra. The dependence of omega(p)(2) on hole concentration p is linear; at p = 1.4 x 10(20) cm(-3), omega(p) is 2150 cm(-1). At each doping, the damping constant gamma is large and corresponds to an infrared hole mobility that is about half the Hall mobility. Secondary-ion mass spectroscopy and localized-vibrational-mode measurements indicate that the Hall-derived p is close to the carbon concentration and that the Hall factor is dose to unity, so that the Hall mobility provides a good estimate of actual de mobility. The observed dichotomy between the de and infrared mobilities is real, not a statistical-averaging artifact. The explanation of the small infrared mobility resides in the influence of intervalence-band absorption on the effective-plasmon damping, which operationally determines that mobility. This is revealed by a comparison of the infrared absorption results to Braunstein's low-p p-GaAs spectra and to a k.p calculation extending Kane's theory to our high dopings. For n-GaAs, which lacks infrared interband absorption, the de and infrared mobilities do not differ.