The optical absorption coefficient of CdZnTe in the near and mid infrared spectral regions was measured at room temperature using FTIR transmission spectroscopy for several x-values in Cd1-xZnyTe grown by the horizontal Bridgman technique as well as for CdTe and ZnTe. The compositional dependence of the absorption coefficient near the band edge was used to determine the composition of bulk CdZnTe, an important material parameter in its application as a substrate for HgCdTe epitaxial growth. In the mid IR range, we find that the wavelength dependence of the absorption coefficient could be varied by adjusting the stoichiometry of the material, i.e., by annealing under various Cd overpressures. The shape of the mid IR Fourier transform infrared spectra is related to the type and the concentration of the free carriers as well as the resistivity of the material. For n-type material, the wavelength dependence of the absorption coefficient can be described by free carrier absorption.