The structures of equal-thickness Co/Re multilayer films and several Co/Re bilayer films have been investigated by X-ray diffraction at low and high angles. Analysis of low-angle reflectivity data from bilayer films indicates that interfacial intermixing is limited to three monolayers and that the two interfacial configurations are different. The high-angle X-ray diffraction data show that multilayer films have coherent interfaces and a highly textured structure with hep  orientations normal to the film plane for periods 21 Å ≤ Λ ≤220 Å. Detailed structures have been determined by fitting the X-ray spectra to calculated ones using a trapezoidal model. The results indicate that samples with 42 Å≤ Λ ≤220 Å have relatively sharp interfaces, in good agreement with the bilayer results. In addition, an out-of-plane expansion of the Co (002) layer is observed in samples with large Λ and results from structural disorder leading to a reduced atomic density. For Λ <21 Å the interfaces arise from the rougher surfaces of the deposited layers.