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Herein, we study hydrogen adsorption on graphene, hexagonal boron nitride (h-BN) and their BNC (boron-nitrogen-carbon) heterostructures by using DFT. Different combinations of carbon and boron nitride moieties in one sheet, as well as the influence of carbon to BN ratio on the hydrogen adsorption, have been systematically investigated. We involve theoretical consideration of adsorption energies (Ea), electrostatic potential maps, independent gradient model analysis as well as Monte-Carlo simulations. We have established that for the 'hollow' adsorption, a minor difference for graphene and BNCs (~ 0.0 (vertical) and 0.1 (horizontal adsorption) kJ/mol) exists, whereas BNCs exhibit sufficiently higher Ea compared with h-BN (0.3 and 0.7 kJ/mol). For the studied 'top' and 'bond' adsorption, changes are more pronounced. The excess reaches 0.4 and 0.9 kJ/mol ('bond'), as well as 0.8 and 1.0 kJ/mol ('top'), for graphene and h-BN, respectively. Hydrogen adsorption isotherms show increased hydrogen uptake by BNCs in comparison with their pristine counterparts.