Semi-inclusive deep inelastic scattering off nuclei is a unique process to study the parton propagation mechanism and its modification induced by the presence of the nuclear medium. It allows us to probe the medium properties, particularly the cold nuclear matter transport coefficient, which can be directly linked to the nuclear gluon density. We present here a model for hadron production in deep inelastic lepton-nucleus scattering, which takes into account the hadronic transverse momentum of final state particles via transverse-momentum dependent parton distributions and fragmentation functions. We implement parton energy loss and hadronic absorption with a geometrical model of the nucleus. The model is compared with the nuclear semi-inclusive deep-inelastic scattering multiplicity ratios and transverse-momentum broadening data from the CLAS, HERMES, and EMC collaborations, aiming for a simultaneous description of these data sets. We obtain a good agreement over the various nuclear targets and the wide kinematical range of those experiments. We best describe the data with a transport coefficient q̂=0.3GeV/fm2, and we highlight the importance and the role of correlations in extracting this quantity. Published by the American Physical Society 2024