The conductivities of an ionic polycrystalline solid lithium iodide (LiI) and covalent, polycrystalline lithium aluminum titanium phosphate (LATP) glass-ceramic material with Al2O3 and Ba0.6Sr0.4TiO3 (0.6BST) additions were investigated. It was determined that blocking and space charge effects coexist in these heterogeneous solids. However, their magnitudes differ from one system to another. The most pronounced blocking effect was evident in the LATP–Al2O3 system, whereas a dominant space charge effect was observed in the LiI–Al2O3 system. The higher dielectric constant of 0.6BST enhanced space charge effect in the LATP–0.6BST system. The space charge effect was also found to be temperature dependent.