Adhesive energy and ultimate adhesive strength of layered TiN/Ti, TiN/ZrN, TiN/Ti/ZrN, and TiN/Zr/ZrN structures are studied by the density functional theory (DFT) and pseudopotentials methods. It has been shown that the TiN/ZrN adhesive depends on the structure of the interface. The maximal energy of adhesion corresponds to the case when titanium atoms of TiN are bound to nitrogen atoms of ZrN, and zirconium atoms of ZrN are bound to nitrogen atoms of TiN. Intercalation of metal layers (Ti or Zr) between TiN and ZrN increase the energy of adhesion; zirconium interlayers influence adhesion more successfully than interlayers of titanium. On example of the TiN/Ti system we studied how energy and force of adhesion depend on structures of the adhesive pairs. We showed that an amorphous coating has smaller values of adhesive energy and ultimate adhesive strength than a crystalline coating, and the roughness of the substrate surface can both improve and to worsen adhesion. Calculated values correlate with known experimental and theoretical data.