A vector spin model is used to show how frustrations within a multisublattice antiferromagnet such as FeMn can lead to fourfold magnetic anisotropies acting on an exchange-coupled ferromagnetic film. Possibilities for the existence of exchange bias are examined and shown to exist for the case of weak chemical disorder at the interface in an otherwise perfect structure. A sensitive dependence on interlayer exchange is found for anisotropies acting on the ferromagnet through the exchange coupling, and we show that a wide range of anisotropies can appear even for a perfect crystalline structure with an ideally flat interface.