A detailed characterization of the impurity centers involved in the photoluminescence (PL) of p-type CdTe doped with arsenic (As) and antimony (Sb) has been performed. The PL spectrum has been measured from 1.35 eV up to the band edge and as a function of temperature (4.2 up to 30 K). In addition to the familiar broad PL line centered at 1.45 eV and present in undoped and doped materials, the doped samples exhibit a new band near 1.54 eV showing a fine structure composed of two peaks whose intensities vary with temperature. The observed longitudinal optical (LO) phonon replicas associated with the zero-phonon lines, at 1.45 eV and 1.54 eV, respectively, are characterized by a Huang-Rhys factor S=1.3±0.1 and S=0.30±0.02. The various electron-hole recombination processes are explained by means of a simple analytic model correlating the position of the zero-phonon lines to the relative intensities of the phonon side bands. The model accounts for the chemical shift of the defect centers and describes the effect of the charge carrier LO-phonon interaction in the framework of the adiabatic approximation within the envelope function approach. Comparison between theory and experiment leads to the following values for the effective Bohr radii: aAs=(10.6±0.1) Å, aSb=(10.3±0.1) Å, and ionization energies: EAs=(58±2) meV, ESb=(61±2) meV. It also leads to conclude to the presence of native shallow donors with binding energy ED=(13±2) meV and of deeper native acceptor complexes with effective Bohr radius aA=(6.1±0.1) Å and ionization energy EA=(157±2) meV.