Accurate measurements of optical properties of multilayer (ML) mirrors and chemical compositions of interdiffusion layers are particularly challenging to date. In this work, an innovative and nondestructive experimental characterization method for multilayers is discussed. The method is based on extreme ultraviolet (EUV) reflectivity measurements performed on a wide grazing incidence angular range at an energy near the absorption resonance edge of low-Z elements in the ML components. This experimental method combined with the underlying physical phenomenon of abrupt changes of optical constants near EUV resonance edges enables us to characterize optical and structural properties of multilayers with high sensitivity. A major advantage of the method is to perform detailed quantitative analysis of buried interfaces of multilayer structures in a nondestructive and nonimaging setup. Coatings of Si/Mo multilayers on a Si substrate with period d=16.4 nm, number of bilayers N=25, and different capping structures are investigated. Stoichiometric compositions of Si-on-Mo and Mo-on-Si interface diffusion layers are derived. Effects of surface oxidation reactions and carbon contaminations on the optical constants of capping layers and the impact of neighboring atoms' interactions on optical responses of Si and Mo layers are discussed.