Infrared reflectivity measurements ͑200-5000 cm Ϫ1 ) and transmittance measurements ͑500-5000 cm Ϫ1 )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 Ϫ1 region and the onephonon band near 270 cm Ϫ1 rides on a progressively increasing high-reflectivity background. An effectiveplasmon/one-phonon dielectric function with only two free parameters ͑plasma frequency p and damping constant ␥) gives a good description of the main features of both the reflectivity and transmittance spectra. The dependence of p 2 on hole concentration p is linear; at pϭ1.4ϫ10 20 cm Ϫ3 , p is 2150 cm Ϫ1 . At each doping, the damping constant ␥ 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 close to unity, so that the Hall mobility provides a good estimate of actual dc mobility. The observed dichotomy between the dc 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 dc and infrared mobilities do not differ.