The impedance of the interface between Li metal anodes and solid electrolytes plays an essential role for the power density of solid-state batteries. We have carried out an impedance spectroscopic study on LGPS-type solid electrolytes in contact to metallic lithium over time periods of several hours. The results reveal that in the case of the highly conductive solid electrolytes Li10GeP2S12, Li10SiP2S12 and Li10Si0.3Sn0.7P2S12, the decomposition layer formed at the interface is a mixed ion-electron conductor (mixed conducting interphase = MCI). The resulting chemical diffusion of Li across the MCI causes a continuous decomposition of the solid electrolyte and a continuous growth of the MCI. From the impedance spectra, we obtain values for the ionic and electronic conductivity of the MCI and for the chemical diffusion coefficient of Li in the MCI. Remarkably, we find that the growth of the MCI is much slower than expected from the chemical diffusion coefficient of Li. This indicates that the growth is not diffusion-controlled, but reaction-controlled. In contrast to the MCI-forming electrolytes, the glass-ceramic 0.95 (0.8 Li2S · 0.2 P2S5) · 0.05 LiI forms a long-term stable solid electrolyte interphase (SEI) in contact to metallic lithium.