Many of the attractive properties of graphene will only be realized when it can be mass produced. One bottleneck is the efficient transfer of graphene between various substrates in nanomanufacturing processes such as roll-to-roll and transfer printing. In such processes, it is important to understand how the ratio of shear-to-tension at the interface between graphene and substrates affects the adhesion energy. With this in mind, this paper examines the mixed-mode adhesive interactions between chemical vapor deposition (CVD) grown graphene that had been transferred to copper or silicon substrates. The approach that was taken was to use blister tests with a range of graphene backing layer materials and thicknesses in order to provide a wide range of the shear-to-tension ratio or fracture mode-mix at the interface. Raman spectroscopy was used to ensure that graphene had indeed been delaminated from each substrate. Measurements of pressure, top surface deflection, and blister diameter were coupled with fracture mechanics analyses to obtain the delamination resistance curves and steady state adhesion energy of each interface. The results showed that the adhesive interactions between graphene and both substrates (Cu and Si) had a strong dependence on the fracture mode-mix. In the absence of plasticity effects, the most likely explanation of this effect is asperity locking from the inherent surface roughness of the substrates.