Thin, fast-conducting and mechanically robust separators are expected to be advantageous in enabling all-solid-state batteries with high energy densities and good electrochemical performance. In this study, a potentially new scalable fabrication route for flexible thiophosphate-polymer separator membranes is demonstrated. By infiltrating a commercially available polymer mesh with the highly conductive inorganic solid ion conductor Li_5.5PS_4.5Cl_1.5, a hybrid separator membrane with a high ionic conductivity is realized. The electrochemical evaluation via rate capability tests reveals superior performance at low stack pressures and high C-rates, when comparing cells employing the hybrid membrane separator, to cells utilizing conventional solid electrolyte separators. As a proof of concept, a full cell implementing the hybrid membrane between a Si-based anode and a LiNi_0.83Co_0.11Mn_0.06O₂-Li_5.5PS_4.5Cl_1.5 composite cathode is evaluated. The experimental work is complemented by resistor network modelling of the hybrid membrane sheets, shedding light on potential challenges in cell operation.