We have measured the anisotropic magnetoresistance of Fe films exchange coupled to antiferromagnetic MnF2 layers. Exchange bias and coercivity obtained from magnetoresistance are in close agreement with superconducting quantum interference device magnetometry data. In addition the magnetoresistance reveals an asymmetry in the magnetization reversal process, despite the fact that the magnetization hysteresis loops show little shape asymmetry. These results correlate well with an earlier study of magnetization reversal asymmetry by polarized neutron reflectometry. The data imply that the magnetization reverses by coherent rotation on one side of the loop and by nucleation and propagation of domain walls on the other.