The interface is well known for taking a critical role in the determination of the functional and mechanical properties of polymer composites. Previous interface research has focused on utilising reduced graphene oxide that is limited by a low structural integrity, which means a high fraction is needed to produce electrically conductive composites. By using 4,4′-diaminophenylsulfone, we in this study chemically modified high-structural integrity graphene platelets (GnPs) of 2–4 nm in thickness, covalently bonded GnPs with an epoxy matrix, and investigated the morphology and functional and mechanical performance of these composites. This covalently bonded interface prevented GnPs stacking in the matrix. In comparison with unmodified composites showing no reduction in electrical volume resistivity, the interface-modified composite at 0.489 vol% GnPs demonstrates an eight-order reduction in the resistivity, a 47.7% further improvement in modulus and 84.6% in fracture energy release rate. Comparison of GnPs with clay and multi-walled carbon nanotubes shows that our GnPs are more advantageous in terms of performance and cost. This study provides a novel method for developing interface-tuned polymer/graphene composites.