Exchange bias in layered CoO/Fe structures is investigated by x-ray resonant magnetic reflectivity (XRMR) measurements. Element-specific hysteresis loops are obtained from x-ray magnetic circular dichroism effects in the XRMR spectra. Evidence is provided for the existence of different types of uncompensated moments in the antiferromagnetic material. Explanations are given for the microscopic nature of these moments and the complex exchange interactions that determine the magnetization reversal in exchange bias systems.