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The asymmetric magnetization reversal in exchange biased Fe/MnF2 involves coherent (Stoner-Wohlfarth) magnetization rotation into an intermediate, stable state perpendicular to the applied field. We provide here the experimentally tested analytical conditions for the unambiguous observation of both longitudinal and transverse magnetization components using the magneto-optical Kerr effect. This provides a fast and powerful probe of coherent magnetization reversal as well as its chirality. Surprisingly, the sign and asymmetry of the transverse magnetization component of exchange biased, low-anisotropy MnF2 and high-anisotropy FeF2 change with the angle between cooling and measurement fields