The Mg ii h & k lines are powerful diagnostics for studying the solar chromosphere. They have become particularly popular with the launch of the Interface Region Imaging Spectrograph (IRIS) satellite, and a number of studies that include these lines have lead to great progress in understanding chromospheric heating, in many cases thanks to the support from 3D MHD simulations. In this study, we utilize another approach to analyze observations: non-LTE inversions of the Mg ii h & k and UV triplet lines including the effects of partial redistribution. Our inversion code attempts to construct a model atmosphere that is compatible with the observed spectra. We have assessed the capabilities and limitations of the inversions using the FALC atmosphere and a snapshot from a 3D radiation-MHD simulation. We find that Mg ii h & k allow reconstructing a model atmosphere from the middle photosphere to the transition region. We have also explored the capabilities of a multi-line/multi-atom setup, including the Mg ii h & k, the Ca ii 854.2 nm, and the Fe i 630.25 lines to recover the full stratification of physical parameters, including the magnetic field vector, from the photosphere to the chromosphere. Finally, we present the first inversions of observed IRIS spectra from quiet-Sun, plage, and sunspot, with very promising results.