We present a theory of nonlinear infrared transmission through and reflection off an antiferromagnetic film with uniaxial anisotropy. In the geometry with the anisotropy axis parallel to the film surface and normal to the plane of incidence, using a linearly polarized wave (TE wave) obliquely incident upon the film, we obtain the transmission and reflection spectra. For an incident intensity available in experiments, the obvious nonlinear effects are seen in the vicinity of the resonant frequency. The nonlinear reflection and transmission can be much stronger or weaker than the linear ones, depending on frequencies or incident angles. The nonlinear interaction also dramatically increases or decreases the absorption of electromagnetic energy in the film.