Ellerman bombs and UV bursts are transient brightenings that are ubiquitously observed in the lower atmospheres of active and emerging flux regions. As they are believed to pinpoint sites of magnetic reconnection in reconfiguring fields, understanding their occurrence and detailed evolution may provide useful insights in the overall evolution of active regions. Here we present results from inversions of SST/CRISP and CHROMIS, as well as IRIS data of such transient events. Combining information from the Mg ii & k, Si iv and Ca ii 8542 Å and Ca ii H & K lines, we aim to characterise their temperature and velocity stratification, as well as their magnetic field configuration. We find average temperature enhancements of a few thousand kelvin close to the classical temperature minimum, similar to previous studies, but localised peak temperatures of up to 10,000-15,000 K from Ca ii inversions. Including Mg ii appears to generally dampen these temperature enhancements to below 8000 K, while Si iv requires temperatures in excess of 10,000 K at low heights, but may also be reproduced with secondary temperature enhancements of 35,000-60,000 K higher up. However, reproducing Si iv comes at the expense of overestimating the Mg ii emission. The line-of-sight velocity maps show clear bi-directional jet signatures for some events and strong correlation with substructure in the intensity images in general. Absolute lineof-sight velocities range between 5-20 km s −1 on average, with slightly larger velocities towards the observer than away. The inverted magnetic field parameters show an enhancement of the horizontal field co-located with the brightenings at heights similar to that of the temperature increase. We are thus able to largely reproduce the observational properties of Ellerman bombs with UV burst signature (e.g. intensities, profile asymmetries, morphology and bi-directional jet signatures) with temperature stratifications peaking close to the classical temperature minimum. Correctly modelling the Si iv emission in agreement with all other diagnostics is, however, an outstanding issue and remains paramount in explaining its apparent coincidence with Hα emission. Fine-tuning the approach (accounting for resolution differences, fitting localised temperature enhancements and/or performing spatially-coupled inversions) is likely necessary in order to obtain better agreement between all considered diagnostics.