The proximity effect in heterostructures formed by the superconducting and ferromagnetic metals is one of the central problems of fundamental metal physics, the solution of which will make it possible to obtain new non-reciprocal electronic components and detectors of electromagnetic radiation. In this work, we create and study point contacts between the two-band superconductor Mo–Re alloy and the strong ferromagnet Ni. We confirm theoretical conclusions about the significant impact of relatively small changes in interface resistance on the current–voltage characteristics of the hybrid contact and discover different degrees of the ferromagnetic electrode effect on two fundamentally distinct superconducting subsystems. The obtained results are useful for developing new hybrid devices based on multiband superconductors.