Interfacial thermal resistance plays a pivotal role in determining the thermal properties and performance of nanostructured materials, where heat transfer is predominantly phonon mediated. We show here that, in addition to the strictly defined interface region, the near interface region can significantly contribute to the overall contact resistance in the case of strongly coupled thermal interface materials. By employing non-equilibrium molecular dynamics simulations we investigate the interfacial thermal transport in a SiC/GaN system relevant to electronics, with a graphene monolayer (as a third material enhancing interfacial thermal transport) confined in between. A previously unexplored, large temperature drop at the near-interface region on the GaN side associated with strong coupling between graphene and the two confining materials is found, indicating that the overall interfacial thermal transport is dominated by the resistance at the adjoining near-interface region and not the interface itself. We further investigate and explain the mechanism behind this finding by analyzing the vibrational properties of junction atoms. The near-interface thermal resistance is found to be dominant when the confined graphene layer is strongly coupled with relatively soft confining materials. Two approaches of interface nanoengineering to effectively reduce the near-interface thermal resistance are also discussed. (C) 2013 Elsevier Ltd. All rights reserved.