We carried out a systematic study of magnetic order and magnetic interlayer coupling in Fe/(Ga,Mn)As bilayers using superconducting quantum interference device magnetometry, polarized neutron reflectometry, element-specific x-ray absorption spectroscopy, x-ray magnetic circular dichroism, and x-ray specular reflectivity. Our results clearly show that Fe/(Ga,Mn)As bilayers are strongly exchange coupled at the interface. However, contrary to recent reports in the literature, we observe a ferromagnetic rather than antiferromagnetic coupling between the magnetic moments of the Mn ions and the Fe layer. It is interesting in this context that the surface region of the (Ga,Mn)As layer that is in direct contact with the Fe film displays a nearly identical coercivity to that of Fe (indicating perfect ferromagnetic coupling of that region), while the bulk of the (Ga,Mn)As layer, which is more weakly ferromagnetically coupled with Fe, shows a significantly smaller coercive field.