A detailed study of exchange-biased Fe∕MnF2 bilayers using magneto-optical Kerr effect shows that the magnetization reversal occurs almost fully through domain wall nucleation and propagation for external fields parallel to the exchange-bias direction. For finite angles ϕ between bias and external field, the magnetization is aligned perpendicular to the cooling-field direction for a limited field range for decreasing fields. For external fields perpendicular to the bias direction, the magnetization aligns with the cooling-field direction for descending and ascending fields before fully reversing. The field range for which the magnetization is close to perpendicular to the external field can be estimated using a simple effective-field model.