Graphene has attracted considerable attention due to the distinguished thermal property to efficiently enhance the thermal transport of polymers. However, high interface thermal resistance (ITR) makes the actual enhancement efficiency of thermal conductivity for graphene/polymer composites below the predicted value. Herein, we proposed to pre-construct the three-dimensional (3D) thermal network in polymer matrix to efficiently reduce the ITR. The electropositive cetyltrimethylammonium bromide (CTAB)-functionalized graphene and the electronegative polydopamine (PDA)-functionalized MWCNT self-assembled to form an interconnected hybrid (CTAB-graphene@PDA-MWCNT) foam with vertical orientation via the directional freezing method. This unique structure provides a shortcut for phonon transmission and endows the obtained composite with the maximum thermal conductivity of 30.09 Wm(-1) K-1 at 9 vol% filler contents. More importantly, PDA at the interface effectively hinders the electron transmission between fillers, resulting in moderate insulation of the prepared composite. (The volume resistivity is 3.2 x 10(6) omega cm.) This demonstrates the prepared composite displays a promising prospect to tackle thermal management problems in modern electronics.