Interlayer exchange coupling (IEC) between two Ga0.95Mn0.05As layers separated by Be-doped GaAs spacers was investigated experimentally using magnetization, magnetotransport and neutron-scattering measurements, which all indicated the presence of robust antiferromagnetic IEC when the GaAs spacer is sufficiently thin. We argue that the observed behavior arises from a competition between the interlayer exchange field and magnetocrystalline anisotropy fields intrinsic to GaMnAs layers.