Epoxies are a class of thermoset polymers which find use in high performance applications. However, epoxies are inherently brittle and are poor conductors of electricity, which limits their ability to be employed in functional applications. Carbon nanomaterials have attracted considerable attention as filler materials, due to their combination of outstanding properties. In the present work, an epoxy polymer was modified with a hybrid nanofiller, consisting of graphene nanoplatelets (GNPs) and carbon nanotubes (CNTs) at a mass ratio of 9:1, using three‐roll milling. Addition of 1 wt% resulted in an increase of eight orders of magnitude in the electrical conductivity and a 182% increase in the fracture energy, GIC, of the epoxy. CNTs contributed greatly in the reduction of the percolation threshold, which was 10 times lower than that of conventional GNP/epoxy composites, while the increase in toughness was entirely attributed to the GNPs, predominantly through the mechanism of crack deflection. The toughening contribution of the hybrid nanofiller was theoretically calculated using analytical modeling, which showed excellent agreement between the predicted and experimental values of GIC.