Mercury telluride (HgTe) thin films with a critical thickness of 6.5 nm are predicted to possess a gapless Dirac-like band structure. We report a comprehensive study on gated and optically doped samples by magnetooptical spectroscopy in the THz range. The quasi-classical analysis of the cyclotron resonance allowed the mapping of the band dispersion of Dirac charge carriers in a broad range of electron and hole doping. A smooth transition through the charge neutrality point between Dirac holes and electrons was observed. An additional peak coming from a second type of holes with an almost density-independent mass of around 0.04m0
was detected in the hole-doping range and attributed to an asymmetric spin splitting of the Dirac cone. Spectroscopic evidence for disorder-induced band energy fluctuations could not be detected in present cyclotron resonance experiments.