We have investigated the magnetic spin structure of a soft-magnetic film that is exchange-coupled to a hard-magnetic layer to form an exchange-spring layer system. The depth dependence of the magnetization direction was determined by nuclear resonant scattering of synchrotron radiation from ultrathin 57Fe probe layers. In an external field a magnetic spiral structure forms that can be described within a one-dimensional micromagnetical model. The experimental method allows one to image vertical spin structures in stratified media with unprecedented accuracy.