As one of the most widely used packaging materials, epoxy composite (EP) offers excellent insulation properties; however, its intrinsic low thermal conductivity (TC) limits its application in high-frequency and high-power devices. To enhance the TC of EP, six highly thermally conductive inorganic fillers, namely, Al2O3, MgO, ZnO, Si3N4, h-BN, and AlN, were incorporated into the EP matrix at varying contents (60-90 wt.%). The resulting epoxy molding compounds (EMCs) demonstrated significant improvement in thermal conductivity coefficient (lambda) at high filler contents (90 wt.%), ranging from 0.67 W m-1 K-1 to 1.19 W m-1 K-1, compared to the pristine epoxy composite preform (ECP, 0.36 W m-1 K-1). However, it was found that the interfacial thermal resistance (ITR) between EP and filler materials is a major hindrance restricting TC improvement. In order to address this challenge, graphene nanosheets (GNSs) and carbon nanotubes (CNTs) were introduced as additives to reduce the ITR. The experimental results indicated that CNTs were effective in enhancing the TC, with the optimized EMC achieving a lambda value of 1.14 W m-1 K-1 using 60 wt.% Si3N4 + 2 wt.% CNTs. Through the introduction of a small amount of CNT (2 wt.%), the inorganic filler content was significantly reduced from 90 wt.% to 60 wt.% while still maintaining high thermal conductivity (1.14 W m-1 K-1). We propose that the addition of CNTs helps in the construction of a partial heat conduction network within the EP matrix, thereby facilitating interfacial heat transfer.