We report magnetization and magetoresistance measurements in hybrid ferromagnetic metal/semiconductor heterostructures comprised of MnAs/(Ga,Mn)As bilayers. Our measurements show that the (metallic) MnAs and (semiconducting) (Ga,Mn)As layers are exchange coupled, re- sulting in an exchange biasing of the magnetically softer (Ga,Mn)As layer that weakens with layer thickness. Magnetoresistance measurements in the current-perpendicular-to-the-plane geometry show a spin valve effect in these self-exchange biased bilayers. Similar measurements in MnAs/p- GaAs/(Ga,Mn)As trilayers show that the exchange coupling diminishes with spatial separation between the layers.