Series of Al2O3(0001)/Pt/(Fe/Pt)n/Pt multilayers with variable number of bilayers n and thicknesses of individual layers were grown using molecular beam epitaxy to investigate influence of buffer layer structure, number of bilayers, and individual layer thickness on their structural and magnetic properties. Both columnar and monocrystalline 10 nm Pt (111) buffer layers were used in the experiment. Structure of Pt buffer layer determined the roughness of Fe/Pt interfaces and consequently magnetic properties of the multilayers. When multilayers were deposited on columnar Pt buffer layer, we observed increase of Fe/Pt interfaces roughness with increasing number of bilayers to values exceeding the nominal Fe/Pt bilayer thickness in the upper part of the sample volume, which resulted in the increment of coercivity in the sample with n = 15 determined from hysteresis loops measured for perpendicular orientation of magnetic field. When Fe/Pt multilayers were deposited on monocrystalline Pt buffer layer, Fe/Pt interfaces were smooth regardless the number of bilayers. All samples, despite of the quality of buffer layer, number of bilayers, and individual layer thickness revealed easy magnetisation axis oriented in the sample plane.