A first-principles electronic structure calculation for Fe/Cr superlattices with layered structures is performed by means of the Korringa-Kohn-Rostoker Green function method within the framework of the local spin density functional formalism. The calculation is carried out for periodic superlattices which consist of ferromagnetic Fe layers and antiferromagnetic or spin-density-wave Cr layers, with magnetizations of two successive Fe layers being aligned parallel or antiparallel, and interlayer magnetic coupling is evaluated by the total energy difference between the parallel and antiparallel couplings. It is shown that the interlayer magnetic coupling oscillates between parallel and antiparallel with a two-monolayer period of the spacer thickness of the Cr layer but the oscillation involves a phase slip around a critical thickness of 16 monolayers, at which the magnetic order in the Cr layer changes from the antiferromagnetic one to the spin-density-wave one. Characteristics of the spin-density-wave order...