We study non-LTE inversions of the Ca II infrared triplet lines as a tool for inferring physical properties of the quiet Sun. The inversion code is successful in recovering the temperature, velocity, and longitudinal magnetic flux density in the photosphere and chromosphere, but the height range where the inversions are sensitive is limited, especially in the chromosphere. We present results of inverting spectropolarimetric observations of the lines in a quiet-Sun region. We find three distinct ranges in chromospheric temperature: low temperatures in the internetwork, high temperatures in the enhanced magnetic network, and intermediate temperatures associated with low magnetic flux regions in the network. The differences between these regions become more pronounced with height as the plasma-β decreases. These inversions support the picture of the chromosphere, especially close to the magnetic network, being highly inhomogeneous in both the vertical and horizontal directions.