All-solid-state lithium batteries (ASSLBs) have gained enormous interest due to their potential high energy density, high performance, and inherent safety characteristics for advanced energy storage systems. Although solid-state ceramic (inorganic) electrolytes (SSCEs) have high ionic conductivity and high electrochemical stability, they experience some significant drawbacks, such as poor electrolyte/electrode interfacial properties and poor mechanical characteristics (brittle, fragile), which can hinder their adoption for commercialization. Typically, SSCE-based ASSLBs require high cell stack pressures exerted by heavy fixtures for regular operation, which can reduce the energy density of the overall battery packages. Polymer–SSCE composite electrolytes can provide inherently good interfacial contacts with the electrodes that do not require high cell stack pressures. In this study, we explore the feasibility of incorporating an electronically and ionically conducting polymer, polypyrrole (PPy), into a polymer backbone, polyvinylidene fluoride-co-hexafluoropropylene (PVDF-HFP), to improve the ionic conductivity of the resultant polymer–SSCE composite electrolyte (SSPE). The electronically conductive polymer-incorporated composite electrolyte showed superior room temperature ionic conductivity and electrochemical performance compared to the baseline sample (without PPy). The PPy-incorporated polymer electrolyte demonstrated a high resilience to high temperature operation compared with the liquid-electrolyte counterpart. This performance advantage can potentially be employed in ASSLBs that operate at high temperatures. In our recent development efforts, SSPEs with optimal formulations showed room temperature ionic conductivity of 2.5 × 10−4 S/cm. The data also showed, consistently, that incorporating PPy into the polymer backbone helped boost the ionic conductivity with various SSPE formulations, consistent with the current study. Electrochemical performance of ASSLBs with the optimized SSPEs will be presented in a separate publication. The current exploratory study has shown the feasibility and benefits of the novel approach as a promising method for the research and development of next-generation solid composite electrolyte-based ASSLBs.