A systematic study of in-plane and out-of-plane exchange biases in FePt/FeMn multilayers epitaxially deposited onto MgO(100), MgO(110), MgO(111) substrates by ion beam sputter-deposition system was performed. It is found that the surface and volume anisotropy constants are largest when samples are growth in (100) direction. While the FePt thickness dependence of the blocking temperature show a similar behavior for samples grown with different crystalline orientations, the dependences of exchange bias field and the unidirectional anisotropy constant on FePt thickness behave differently for different orientations. The ratio of in-plane and out-of-plane exchange biases is not only strongly dependent on crystalline orientation but also on thickness of FePt layers suggesting that the spin structure at the interface in multilayer thin films may not be the same as that of the antiferromagnetic bulk.