Radiation is almost completely reflected within the exciton-polariton stop band of a semiconductor, as in the typical case of CuCl. We predict, however, that a coherently driven exciton-biexciton transition allows for the propagation of a probe light beam within the stop band. The phenomenon is reminiscent of electromagnetically induced transparency effects occurring in three-level atomic systems, except that it here involves delocalized electronic excitations in a crystalline structure via a frequency and wave-vector selective polaritonic mechanism. A well-developed transparency, favored by the narrow linewidth of the biexciton, is established within the stop band where a probe pulse may propagate with significant delays. The transparency window can be controlled via the pump beam detuning and intensity.