This is a theoretical investigation of the exchange bias phenomenon, and the properties of a thin magnetic film's magnetization hysteresis loop, on the rough surface of a hard-magnetic antiferromagnet. An interface model with a periodic structure of atomic steps is presented. These atomic steps are associated with a spatially inhomogeneous distribution of the ferromagnetic film magnetization, akin to a system of domain walls. This structure leads to a complicated external field dependence of magnetization: the hysteresis curve can assume an asymmetrical shape and "fall apart" into two hysteresis loops, divided by a "horizontal plateau," or an area with constant field-independent magnetization. Such field dependence behavior has been recently observed experimentally in different ferro/antiferromagnet systems. The field dependence of magnetization has been obtained analytically using the long-wave approximation for various characteristics of ferromagnetic film (its thickness, values of exchange interaction, and magnetic anisotropy), and the interface (the period of the inhomogeneous structure, and exchange interaction through the interface). The analytical results are confirmed by numerical calculations for the corresponding discrete model with a more complex interface structure.