A model giving a qualitative explanation of the results of an experimental investigation of the field dependences of the magnetization in ferro- and antiferromagnetic media in contact with one another is proposed. In this model a thin ferromagnetic (FM) film with strong easy-plane anisotropy is described in the continuum approximation. It is shown that collinear and canted structures of the ferromagnetic layer can co-exist in the system studied. The ranges of the parameters (exchange interactions in the FM layer and through the FM/AFM interface, thickness of the FM layer, and magnitude of the external magnetic field) where a nonuniform state of the FM exists are found and explicit analytic expressions are obtained for the distribution of the magnetization in this state. The dependences of the total magnetization of the system on the magnitude of the external field are constructed in the physically important cases of "thin" and "thick" FM layers, and it is demonstrated that the experimentally observed unsymmetric dependence M (H) is possible. The results of the present work are compared with our previous results obtained using simpler model of a two-layer FM subsystem.