Nanoscale multilayer coating (NMC) based on Zr/Nb layers (100/100 nm) before and after H+ irradiation was investigated by combining experimental techniques with first-principles calculations. Detailed studies of structural and phase state and defect structure of Zr/Nb NMC were performed using methods of transmission electron microscopy, X-ray structural analysis, glow discharge optical emission spectrometry, and the Doppler broadening spectroscopy using variable energy positron beam. The first-principles calculations of binding energies for hydrogen in metal Zr/Nb layers was carried out by the pseudopotential method within the density functional theory framework. First-principles calculations and experimental data indicate the presence of macro- and microstrains predominantly in the zirconium layers of Zr/Nb NMC. The main feature of the studied Zr/Nb NMC is the predominant hydrogen localization in Zr layers near the interfaces. The annihilation of positrons is shown to occur mainly in the Zr layers in the vicinity of the interface.