Different classes of solid electrolytes for all-solid-state batteries (ASSB) are currently being investigated, with each of them suitable for a different ASSB concept. Their combination in hybrid battery cells enables the use of their individual benefits while mitigating their disadvantages. The cubic stuffed garnet Li₇La₃Zr₂O₁₂ (LLZO), for example, is stable in contact with metallic lithium but has only moderate ionic conductivity, whereas the thiophosphate Li₁₀SnP₂S₁₂ (LSPS) is processable using conventional battery manufacturing technologies and has an excellent lithium-ion conductivity but an inferior electrochemical stability. In this work, we, therefore, present a layered hybrid all-solid-state full-cell concept that accommodates a lithium metal anode, a LiNi_0.8Co_0.1Mn_0.1O₂-based composite cathode with an LSPS catholyte (LSPS/NCM811) and a sintered monolithic LLZO separator. The electrochemical stability of LLZO and LSPS at cathodic potentials (up to 4.2 V) was investigated via cyclic voltammetry in test cells, as well as by cycling half cells with LSPS or a mixed LSPS/LLZO catholyte. Furthermore, the pressure-dependency of the galvanostatic cycling of a Li | LLZO | LSPS/NCM811 full cell was investigated, as well as the according effect of the Li | LLZO interface in symmetric test cells. An operation pressure of 12.5 MPa was identified as the optimal value, which assures both sufficient inter-layer contact and impeded lithium penetration through the separator and cell short-circuiting.