The high energy density characteristic of the all-solid-state battery technology makes it one of the promising competitors of current liquid electrolyte-based lithium-ion batteries. However, due to the low ionic conductivity of solid materials and existing issues in active material-solid electrolyte interfaces, all-solid-state batteries show strong nonlinear behavior when the amplitude of input current is relatively high. In this paper, we have developed a methodology based on block-oriented nonlinear systems that can detect, quantize, and model the battery behavior, accurately. For this purpose, two solid-state coin cells, which have different ionic conductivity at the cathode interface are manufactured and excited with multisine input current. The Best Linear Approximation (BLA) method has been used to separate linear frequency response function (FRF) from nonlinear distortion. Then, a Hammerstein-Wiener system has been developed and parametrized to model the nonlinear distortions caused by ionic conductivity variation of the solid electrolyte at the cathode layer. Furthermore, the developed model has been utilized to detect possible faults in the electrode-electrolyte interface based on the nonlinearity level of the measured voltage.