Within the framework of a periodic Anderson model, calculations of the magnetic moments at Fe and Cr atoms and the energy of antiferromagnetic and ferromagnetic ordering of Fe layers in a superlattice were carried out for an Fe/Cr multilayer system with disordered-alloy interfacial layers. It is shown that a suppression of the antiferromagnetic order occurs with increasing intermixing at the interfaces. To study alloying at an interface, an algorithm for simulating the atomic intermixing at an interface during epitaxial growth was developed. The results of self-consistent calculations of magnetic moment distributions for the simulated structures demonstrate the dependence of magnetic properties on the degree of atomic intermixing in the interface. The distributions of magnetic moments in the Fe-Cr and Cr-Fe interfaces prove to be substantially different. It is shown that an increase in the intermixing parameter results in an interface broadening, a broader range of the variation of magnetic moments at iron atoms, and a change in the type of the nearest-neighbor configuration of Fe atoms.