Understanding the interfacial properties between an atomic layer and its substrate is of key interest at both the fundamental and technological level. From Fermi level pinning to strain engineering and superlubricity, the interaction between a single atomic layer and its substrate governs electronic, mechanical, and chemical properties of the layer-substrate system. Here, we measure the hardly accessible interfacial transverse shear modulus of an atomic layer on a substrate. We show that this key interfacial property is critically controlled by the chemistry, order, and structure of the atomic layer-substrate interface. In particular, the experiments demonstrate that the interfacial shear modulus of epitaxial graphene on SiC increases for bilayer films compared to monolayer films, and augments when hydrogen is intercalated between graphene and SiC. The increase in shear modulus for two layers compared to one layer is explained in terms of layer-layer and layer-substrate stacking order, whereas the increase with H-intercalation is correlated with the pinning induced by the H-atoms at the interface. Importantly, we also demonstrate that this modulus is a pivotal measurable property to control and predict sliding friction in supported two-dimensional materials. Indeed, we observe an inverse relationship between friction and interfacial shear modulus, which naturally emerges from simple friction models based on a point mass driven over a periodic potential. This inverse relation originates from a decreased dissipation in presence of large shear stiffness, which reduces the energy barrier for sliding.