Amplitude-division beam splitters for XUV radiation sources have been developed and extensively characterized. Mo/Si multilayer coatings were deposited on 50 nm-thick SiN membranes. By changing the multilayer structure (periodicity, number of bilayers, etc.) the intensity of the reflected and transmitted beams were optimized for selected incident radiation parameters (wavelength, incident angle). The developed optical elements were characterized by means of XUV reflectometry and transmission measurements, atomic force microscopy and optical interferometry. Special attention was paid to the spatial homogeneity of the optical response and reflected beam wavefront distortions. Here the results of the characterization are presented and improvements required for advanced applications at XUV free-electron lasers are identified. A flatness as low as 4 nm r.m.s. on 3 × 3 mm beam splitters and 22 nm r.m.s. on 10 × 10 mm beam splitters has been obtained. The high-spatial-frequency surface roughness was about 0.7-1 nm r.m.s. The middle-spatial-frequency roughness was in the range 0.2-0.8 nm r.m.s. The reflection and transmission of the beam splitters were found to be very homogeneous, with a deviation of less than 2% across the full optical element.