The magnetic properties of multilayers of ferromagnetic EuS intercalated with diamagnetic PbS were studied as a function of the EuS layer thickness (varying from 2 to 200 ML). The critical temperature $T_C$ of the paramagnet-ferromagnet phase transition was determined from magnetization vs temperature measurements and was found to depend on the underlying substrate [KCl (100) vs ${\mathrm{BaF}}_2$ (111)] as well as on the thickness of the EuS layer. For thick layers ${(d}_{\mathrm{EuS}}\approx 200\hspace{0.5em}\mathrm{ML}),$ which mimic semibulk EuS, the $T_C$ values were found shifted with respect to the bulk EuS (about 1 K up for layers grown on KCl and about 3 K down for layers grown on ${\mathrm{BaF}}_2).\mathrm{}$ This effect is attributed to stress resulting mainly from the difference of thermal expansion coefficients between the substrate and the structure. For thin layers ${(d}_{\mathrm{EuS}}<10\mathrm{}\hspace{0.5em}\mathrm{ML}),$ a systematic reduction of $T_C$ with decreasing EuS layer thickness was observed. This behavior is discussed from two points of view: (a) the reduction of the average number of magnetic neighbors because of the increasing role of the interface for the thin layers, and (b) the three-dimensional/two-dimensional (3D/2D) crossover from a 3D Heisenberg-type ferromagnet to a 2D XY or Ising-like system. The dependence of the magnetic anisotropy on the EuS layer thickness was studied by ferromagnetic resonance measurements. The energy of magnetic anisotropy can be well described as a sum of a thickness-independent (volume) part and a ${1/d}_{\mathrm{EuS}}$ (surface) term. We found that EuS layers with $d_{\mathrm{EuS}}>2\mathrm{}\hspace{0.5em}\mathrm{\AA }\mathrm{}$ magnetize in the plane of the structure.