Solid-state lithium batteries are considered one of the most promising candidates for future electrochemical energy storage. However, both inorganic solid electrolytes (such as oxide-based or sulfide-based materials) and polymer electrolytes still have to overcome several challenges to replace the currently used liquid organic electrolytes. An increasingly adopted approach to overcome these challenges relies on the combination of different electrolyte systems. Herein, we report the synthesis and characterization of a novel sulfur-doped single-ion conducting multi-block copolymer (SIC-BCE) system. This SIC-BCE may serve as interlayer between the electrodes and the sulfidic electrolyte such as Li6PS5Cl, thus benefitting of the high ionic conductivity of the latter and the favorable interfacial contact and electrochemical stability of the polymer. The polymer shows excellent ionic conductivity when swollen with ethylene carbonate and allows for stable stripping/plating of lithium, accompanied by a suitable electrochemical stability towards reduction and oxidation. First tests in symmetric Cu|SIC-BCE|Li6PS5Cl|SIC-BCE|Cu cells confirm the general suitability of the polymer to stabilize the electrode|electrolyte interface by preventing the direct contact of the sulfidic electrolyte with, e.g., metallic copper foils.