We report x-ray magnetic circular dichroism and superconducting quantum interference device magnetometry experiments to study magnetic order and coupling in thin Fe/(Ga, Mn)As(100) films. We observe induced magnetic order in the (Ga, Mn)As layer that extends over more than 2 nm, even at room temperature. We find spectroscopic evidences of a hybridized d configuration of Mn atoms in Fe/(Ga, Mn)As, with negligible Mn diffusion and/or MnFe intermixing. We show by experiment as well as by theory that the magnetic moment of the Mn ions couples antiparallel to the moment of the Fe overlayer.