The article is dedicated to reveling the reason of unusual magnetic properties, found in one of Co/Dy periodic multilayer systems with different Co/Dy layer thickness by X-Ray reflectivity, scanning/transmission electron microscopy together with energy dispersive X-Ray microanalysis. Magnetic measurements did not demonstrate any peculiarities in the system with thinner Co/Dy layer thickness. However, the system with thicker layers demonstrated an anomalous behavior of the perpendicular magnetic anisotropy. Based on X-Ray reflectivity measurements, it was found that the polarizability value in the system with thicker Co/Dy layer was very high and related to glassy intermetallic DyCo2 compound formation. Electron microscopy and microanalysis data also indicated the presence of glassy intermetallic DyCo2 layers, which could be responsible for the peculiar magnetic behavior. The relation between magnetic properties and microstructure was revealed.