Electronic transport models for conducting polymers (CPs) and blends focus on the arrangement of conjugated chains, while the contributions of the nominally insulating components to transport are largely ignored. In this work, an archetypal CP blend is used to demonstrate that the chemical structure of the non-conductive component has a substantial effect on charge carrier mobility. Upon diluting a CP with excess insulator, blends with as high as 97.4 wt % insulator can display carrier mobilities comparable to some pure CPs such as polyaniline and low regioregularity P3HT. In this work, we develop a single, multiscale transport model based on the microstructure of the CP blends, which describes the transport properties for all dilutions tested. The results show that the high carrier mobility of primarily insulator blends results from the inclusion of aromatic rings, which facilitate long-range tunneling (up to ca. 3 nm) between isolated CP chains. This tunneling mechanism calls into question the current paradigm used to design CPs, where the solubilizing or ionically conducting component is considered electronically inert. Indeed, optimizing the participation of the nominally insulating component in electronic transport may lead to enhanced electronic mobility and overall better performance in CPs.