The magnetic properties of heterostructures consisting of two films are studied. The upper layer involves rare-earth intermetallic nanostructured superlattices consisting of exchange-coupled layers (TbCo2/FeCo)n (TCFC), and the lower layer includes either epitaxial manganite La0.7Sr0.3MnO3 (LSMO) with optimum strontium doping or an epitaxial film of an yttrium–iron garnet Y3Fe5O12 (YIG) with a Bi additive. TCFC is a ferromagnet having high Curie temperature and provides controllable induced magnetic anisotropy. Experimental studies showed that the interlayer interaction of the TCFC/LSMO heterostructure is antiferromagnetic. There was an increase in the FMR line width in the structures due to the flow of a spin current through the interface between two films. There was electric voltage in the TCFC/YIG heterostructure induced in the TCFC intermetallide film, due to an inverse spin Hall effect under ferromagnetic resonance conditions.