Magnetic and structural properties of EuS/Co multilayers were studied by magnetic optical Kerr effect and SQUID magnetometry techniques and by X-ray diffraction method. The multilayers containing monocrystalline, ferromagnetic EuS layer (thickness 35-55Å) and metallic Co layer (thickness 40-250Å), were grown on KCl (001) and BaF2 (111) substrates using high vacuum deposition technique employing electron guns for Co and EuS. All investigated EuS/Co multilayers exhibit ferromagnetic properties at room temperature due to Co layer with the ferromagnetic transition in EuS layer clearly marked upon cooling below 16 K. In EuS/Co/EuS trilayers grown on KCl substrate the antiferromagnetic alignment of magnetization vectors of Co and EuS layers was experimentally observed as a characteristic low field plateau on magnetization hysteresis loops and a decrease in multilayer magnetization below 16 K. In Co/EuS bilayers the characteristic temperature dependent shift of magnetization loops was found due to exchange bias effect attributed to the CoO/Co interface formed by the oxidation of the top Co layer.