Adhesion interaction of epoxy resin with the basal surfaces of h-BN and graphite is investigated with the first-principles density functional theory calculations in conjunction with the dispersion correction. The h-BN/epoxy and graphite/epoxy interfaces play an important role in producing nanocomposite materials with excellent thermal dissipation properties. The epoxy resin structure is simulated by using four kinds of fragmentary models. Their structures are optimized on the h-BN and graphite surfaces after an annealing simulation. The distance between the epoxy fragment and the surface is about 3 Å. At the interface between h-BN and epoxy resin, no H-bonding formation is observed, though one could expect that the active functional groups of epoxy resin, such as hydroxyl (−OH) group, would be involved in a hydrogen-bonding interaction with nitrogen atoms of the h-BN surface. The adhesion energies for the two interfaces are calculated, showing that these two interfaces are characterized by almost the same strength of adhesion interaction. To obtain the adhesion force–separation curve for the two interfaces, the potential energy surface associated with the detachment of the epoxy fragment from the surface is calculated with the help of the nudged elastic band method and then the adhesion force is obtained by using either the Morse-potential approximation or the Hellmann–Feynman force calculation. The results from both methods agree with each other. The maximum adhesion force for the h-BN/epoxy interface is as high as that for the graphite/epoxy interface. To better understand this result, a force-decomposition analysis is carried out, and it has been disclosed that the adhesion forces working at both interfaces mainly come from the dispersion force. The trend of increase in the C 6 parameters used for the dispersion correction for the atoms included in the h-BN or graphite surface is in the order: N < C < B, which reasonably explains why the strengths of the dispersion forces operating at the two interfaces are similar. Also, the electron localization function analysis can explain why the h-BN surface cannot form an H bond with the hydroxyl group in epoxy resin.