Heat dissipation efficiency and electromagnetic interference (EMI) shielding performance are vital to integration, miniaturization, and application of electronic devices. Flexible and designable polymer-based composites are promising candidates but suffer from unavoidable interfacial thermal resistances, anisotropic thermal conductivity, and low shielding of EMI limiting application. Herein, multifunctional epoxy resin (EP)-based composites with an interconnected carbon fibers (CFs) network structure containing a low thermal resistance interfacial were prepared by high-temperature calcination and infiltration. The coherent heat and electron transfer pathways constructed with self-oriented CFs cloth connected by carbon nanotubes (CNTs) converted from leaf-shaped zeolitic imidazolate frameworks (ZIF-L) and stable magnetic property provided by cobalt nanoparticles contained in the CNTs made composites to an integrated in-plane thermal conductivity of up to 7.50 W m −1 K −1 , a through-plane thermal conductivity of 1.96 W m −1 K −1, and an EMI shielding effectiveness of 38.4 dB. Furthermore, the mechanical properties of CFs and the junction effect of CNTs endowed the composites with stability of mechanical property, thermal conductivity, and EMI shielding effectiveness after multiple bendings. The finite element simulation further verified the advantage of CFs network linked by CNTs on heat transfer. This work provides the desired design for the construction of a multifunctional polymer-based composite used in advanced electronic equipment.