All-solid-state Li+ batteries have a number of advantages over traditional batteries with a liquid electrolyte. One of the key problems related to their creation is the choice of compatible materials. In this work, the chemical and thermal stability of Li1.5Al0.5Ge1.5(PO4)3 solid electrolyte versus Li4Ti5O12 anode was studied. Nanostructured Li4Ti5O12 powder with the mean particle size of about 500 nm was synthesized by sol-gel method. NASICON-type structured Li1.5Al0.5Ge1.5(PO4)3 solid electrolyte obtained by the crystallization of the monolithic glass exhibits a high lithium-ion conductivity (5·10−4 S cm−1 at 25 °C) and a compact microstructure. The thermal behavior of their mechanical mixture and the resistance of the solid electrolyte|electrode half-cells were investigated. The influence of Li3BO3 addition on the interface between the solid electrolyte and composite anode is also discussed. According to DSC data, the interaction of Li1.5Al0.5Ge1.5(PO4)3 with Li4Ti5O12 begins at 545 °C, while Li3BO3 leads to a slight increase in their thermal stability up to 632 °C. It was established that Li2TiO3 and TiO2 impurities are formed after annealing the Li1.5Al0.5Ge1.5(PO4)3:Li4Ti5O12 mixture at 600 and 700 °C. However, Li3PO4 and AlPO4 phases begin to appear after annealing the studied mixture at 800 °C. In case of the Li3BO3-containing mixture, Li4B2O5, Li3PO4, LiTi2O4 and AlPO4 phases are formed only after annealing at 700 °C, while heating at 800 °C leads to the complete degradation of the Li1.5Al0.5Ge1.5(PO4)3 solid electrolyte. The resistance of the cells with Li4Ti5O12 anode decreases when the annealing temperature rises from 500 to 800 °C. The introduction of Li3BO3 into the composite anode leads to an increase in the interface resistance under the same heat treatment conditions.