We propose a promising electrochemical analysis tool based on the distribution of relaxation times (DRT) to quantify interfacial resistances towards a comprehensive understanding of complex solid-state interfacial phenomena in sulfide-based all-solid-state batteries (ASSBs). Using DRT-assisted impedance analysis, we identify a new resistance component in the range of 102-103 Hz of 3.5 and 0.9 Ω in the absence and presence of a LiNbO3 layer, respectively, at 1C-rate. Experimental and computational studies confirm that this interfacial resistance results from lithium depletion in sulfide solid electrolytes. Furthermore, we expect our approach to provide new insights into complex interfacial phenomena in ASSBs.