We measured directly the depth-dependent Fe spin rotation upon magnetization reversal in exchange-coupled Fe/MnF2 bilayers using nuclear resonant scattering of synchrotron radiation from an 57Fe-probe layer buried at different depths within the Fe film. Our results show that the exchange-biased ferromagnetic layer develops a noncollinear spin structure along the film normal direction, reminiscent of a partial domain wall parallel to the Fe/MnF2 interface. This is contrary to most theoretical models of exchange bias which assume a collinear spin structure in the ferromagnetic layer.