We investigate the depth-dependent magnetization reversal and spin structure of Fe/NiO epitaxial bilayers before and after field cooling. Using nuclear resonant scattering of synchrotron radiation we selectively probe the spin structure of the interfacial layers in contact with NiO. We provide a direct evidence that magnetization reversal involves a rotation in the film plane perpendicular to the applied field, except for the interfacial Fe layers. Moreover, we show that the spin structure of the ferromagnetic layer is not modified by field cooling and that the exchange bias in the Fe layer is independent of the distance from the antiferromagnetic phase.