A theoretical investigation is reported of the coherent nonlinear response of excitons and biexcitons in a thin semiconductor film subjected to resonant laser radiation. It is shown that saturation of an exciton transition results in an abrupt qualitative change in the nature of film transition from the regime of total reflection of the incident pulse at low pump amplitudes to oscillatory reflection at high amplitudes. A new area theorem is derived for ultrashort pulses: it establishes a correspondence between the areas of the incident, transmitted and reflected pulses. Anomalous transmission and reflection is predicted for large values of the nonlinear parameter. The equations of the state, describing bistable behavior of the amplitudes of the fields of the transmitted and reflected radiation, are derived for quasi-cw operation.