In order to study exchange coupling and spin distributions at atomically abrupt ferromagnetic/antiferromagnetic interfaces, we construct lattice-matched Co/Cr multilayer models. Here we consider strained-layer superlattices composed of alternating regions of ferromagnetic bcc Co and antiferromagnetic bcc Cr with repeat periods ranging from four to eight atomic layers. For computational simplicity, Cr is represented by a theoretically stabilized commensurate antiferromagnetic spin arrangement. The multilayer spin distributions are determined by carrying out first-principles self-consistent spin-polarized LMTO/ASA electronic structure calculations. We find that the magnetic properties of the Co/Cr superlattices are dominated by the ferromagnetic Co layers, though the antiferromagnetic character of bcc Cr is still evident. For multilayers containing one Co layer and three to seven Cr layers per repeat period, there is only one stable spin arrangement corresponding to ferromagnetic coupling across the Co/Cr interfaces. For superlattices containing thicker Co regions, e.g., three Co layers and five Cr layers, there are two distinct spin arrangements corresponding to ferromagnetic as well as antiferromagnetic coupling across the Co/Cr interfaces. The implications of these results for more complicated Co/Cr multilayers are discussed.