The magnetization profile that forms in the soft part of an exchange-coupled hard/soft bilayer submitted to a rotating in-plane magnetic field has been studied both theoretically and experimentally. The evolution of the stable magnetic configurations as a function of the field orientation has been determined from micromagnetic calculations, for varying strength of the rotating field. The anisotropic magnetoresistance associated with these configurations has been deduced and compared with experimental results obtained on a TbFe/GdFe ferrimag-netic bilayer. A good agreement is obtained between calculated and measured data, without any parameter adjustment. As the applied field is rotated, a twisted magnetization distribution of Bloch type develops in the soft GdFe layer. The simulations show the existence of several possible stable magnetic profiles. These differ either by the amount of magnetization twist only or by the amount of twist and the chirality of the profile. Transport measurements allow one to determine which configuration is actually adopted by the system and in what circumstances the system switches from one configuration to another. Two types of transition are identified. The first one is related to the existence of a hard axis of magnetization in the GdFe layer. The second one corresponds to a change of chirality of the wall.