By using first-principles methods, we perform a theoretical investigation of adsorption of hydrogen molecules between bilayer solid matrix layers (bilayer boron nitride sheets (BBN) and graphene/boron nitride heterobilayers (GBN)) with variable interlayer distance (ILD). We find that the H-2 adsorption energy has a minimum by expanding the interlayer spacing, along with further interlayer expansion, arising from many H-2 binding states and electrostatic interaction induced by the polar nature of B-N bonds. To determine if successive addition of H-2 molecules is indeed possible using the minimal H-2 adsorption energy as the reference state, we then simulate the hydrogen storage capacity of BBN and GBN with different stacking types, and find that the GBN with Bernal stacking is superior for reversible hydrogen storage. Up to eight H-2 molecules can be adsorbed with the average adsorption energy of -0.20 eV/H-2, corresponding to similar to 7.69 wt % hydrogen uptake. Copyright (C) 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.