Non-covalent interactions such as hydrogen bonding and π-π stacking are essential types of interactions governing molecular self-assembly. The π-π stacking ability of aromatic rings depends on the electron density of the π orbitals, which is affected by the electron-withdrawing or electron-donating properties of the substituents. We have here studied the effect of hydrogen bonding on the strength of the π-π stacking interactions by calculating the binding energies at the explicitly correlated Møller-Plesset (MP2-F12) perturbation theory level using polarized triple-ζ quality basis sets. The stacking interactions in the presence of hydrogen bonding are found to be stronger than in the absence of the hydrogen bonding suggesting that hydrogen bonds lead to π depletion, which affects the aromatic character of the aromatic rings and increases the strength of the π-π stacking interaction. We have also studied how hydrogen bonding affects the stacking interaction by calculating local orbital locator integrated pi over plane (LOLIPOP) indices. Comparing LOLIPOP indices with the stacking-interaction energies calculated at the MP2-F12 level shows that there is no clear correlation between the stacking-interaction energies and LOLIPOP indices.