To understand the role of alumina interlayer in the adhesion of ZrN coating on U-Mo surface using atomic layer deposition technique, we investigate the interfaces of ZrN/U, Al2O3/U, and ZrN/Al2O3 using first-principles density-functional theory calculations. The preferred interfacial plane orientation relationships and terminations for all the interfaces are predicted. Calculations show that both lattice mismatch and interfacial bonding play crucial roles in determining the adhesion strength of ZrN and Al2O3 coatings on U metal surface. The strength of Al2O3/U and ZrN/Al2O3 interfaces are found to be substantially higher than that of ZrN/U interface. The strong interfacial adhesion of Al2O3/U and ZrN/Al2O3 interfaces is ascribed to the formation of ionic bonds at the interface, as compared to weak metallic bonds formed in ZrN/U interface. Therefore, the formation of metaloxygen ionic bonds at interface explains the role of alumina layer in the improved adhesion of ZrN coating on U-Mo surface.