Developing solid-state batteries (SSB) with a lithium metal electrode (LME) using only one type of solid electrolyte (SE) is a significant challenge since no SE fits all the requirements imposed by both electrodes. A possible solution is using multilayer SSBs with an LME where the drawbacks of each SE are overcome by using layers of different SEs. However, research on inorganic SE1|SE2 heteroionic interfaces is still quite preliminary, especially regarding oxide|sulfide heteroionic interfaces. This work reports the electrochemical investigation of the heteroionic interface between Li6.25Al0.25La3Zr2O12 (Al-LLZO) and two representative materials for sulfide-based SEs: argyrodite-based Li6PS5Cl (LPSCl) and glass-like Li7P3S11 (LPS711). Through in-depth temperature- and pressure-dependent impedance analyses of multilayer symmetric cells at equilibrium (i.e., no current load), the electrical properties of the heteroionic interfaces are assessed. The pressure-dependent kinetic of the Al-LLZO|LPSCl pair is interpreted with the concept of geometric constriction resistance and show that its resistance is lower than for the Al-LLZO|LPS711 pair. Furthermore, the effect of Al-LLZO surface treatment on the electrical properties of the Al-LLZO|LPSCl heteroionic interface is evaluated. Such investigation shows that the value of the interface activation energy decreases when the Al-LLZO surface is heat treated, revealing a significant influence of the carbonate/hydroxide passivation layer on the heteroionic interface. Additionally, by cycling the symmetric cell for 900 h at 1.0 mAh·cm-2, it is revealed that the Al-LLZO|LPSCl interface has a lower impedance increase than the Al-LLZO|LPS711 interface, especially if the Al-LLZO is heat treated. With this work, we highlight that the oxide|argyrodite combination can be a promising candidate for multilayer SSBs with an LME. However, we show that an optimized LLZO surface treatment and chemical analysis of the interface are recommended for future research.