The need for conducting polymeric materials in applications such as flexible electronics is on the rise. Immiscible blends containing conducting particles offer a generic route to tune the electrical functionality by means of tailoring their morphology combined with selective localization of the particles. The conductivity of biphasic blends consisting of PáMSAN and PMMA containing multiwall carbon nanotubes (MWNTs) was enhanced by tailoring the blend morphology with a PS-PMMA copolymer. The PáMSAN/PMMA blends undergo phase separation by spinodal decomposition during which the MWNTs preferentially localize in the PáMSAN phase. The effects of the architecture (block or random) and molecular weights of the copolymers on the morphology, linear viscoelastic moduli and the resulting blend conductivity were systematically investigated at various copolymer concentrations. Effective compatibilization is achieved with block copolymers independent of their molecular weight. Short random copolymers are not effective, whereas long random copolymers are as effective as the long block copolymers. An effective compatibilizer led to interfacial tension mediated suppression of coarsening of the PáMSAN domains, resulting in increased connectivity and refinement of the PáMSAN phase containing the MWNTs, as confirmed by optical microscopy and the linear viscoelastic response of the blends. A pronounced increase by 3 decades in magnitude of the low frequency electrical conductivity was achieved upon addition of only 0.25 wt% long random copolymer to blends with 0.5 wt% MWNTs. Furthermore, the copolymer concentration required to develop a percolating network of MWNT-MWNT and PáMSAN-MWNT are approximately the same, independent of the type and molecular weight of the copolymer, suggesting that the electrical and rheological percolations are comparable. In conclusion, the ability of the copolymer to refine and stabilize the PáMSAN domains governs the blends electrical conductivity.