The complexes formed by hydrogen with metal hydrides (LiH, NaH, BeH2, MgH2, BH3, AlH3, Li2H2, Na2H2, Be2H4, and Mg2H4) have been theoretically studied at the MP2/aug-cc-pVTZ, MP2/aug-cc-pVQZ and CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ levels of theory. The hydrogen molecule can act as a Lewis acid or base. In the first case, a dihydrogen bonded complex is obtained and in the second an interaction between the sigma-bond of the hydrogen molecule and an empty orbital of the metal atoms is found. Quantum theory of atoms in molecules and natural bond orbitals methods have been applied to analyze the intermolecular interactions. Additionally, the cooperativity effects are analyzed for selected complexes with two H-2 molecules where both kinds of interactions exist simultaneously.