We report the antiferromagnetic (AFM) interlayer exchange coupling between Ga0.97Mn0.03As ferromagnetic semiconductor layers separated by Be-doped GaAs spacers. Polarized neutron reflectivity reveals a characteristic splitting at the wave vector corresponding to twice the multilayer period, indicating that the coupling between the ferromagnetic layers is AFM. When the applied field is increased to above the saturation field, this AFM coupling is suppressed. This behavior is not observed when the spacers are undoped, suggesting that the observed AFM coupling is mediated by doped charge carriers.