A first-principles Green's function technique has been used to investigate the magnetic interlayer coupling and the electronic structure responsible for the magnetic interaction in a bcc system. We discuss the close relation between the interlayer coupling, the bulk Fermi surface of the spacer material, and the dispersion of the quantum-well states in the two-dimensional Brillouin zone. As a function of spacer thickness, we find an oscillatory long-range energy splitting of Fe/Cu interface states which is shown to be an example of a long-range oscillatory interface interaction transmitted by the spin-polarized quantum-well states of the Cu spacer. These interacting interface states may provide a signature of the magnetic coupling in multilayers.