We employ Faraday and Kerr effect spectroscopy in the infrared range to investigate the electronic structure of Ga_{1-x}Mn_{x}As near the Fermi energy. The band structure of this archetypical dilute-moment ferromagnetic semiconductor has been a matter of controversy, fueled partly by previous measurements of the unpolarized infrared absorption and their phenomenological impurity-band interpretation. Unlike the unpolarized absorption, the infrared magneto-optical effects we study are intimately related to ferromagnetism, and their interpretation is much more microscopically constrained in terms of the orbital character of the relevant band states. We show that the conventional theory of the disordered valence band with an antiferromatnetic exchange term accounts semiquantitatively for the overall characteristics of the measured infrared magneto-optical spectra.