Electromigration (EM) in power distribution networks (PDNs) is a major reliability issue in 3D ICs. While the EM issues of local vias and through-silicon-vias (TSV) have been studied separately, the interplay of TSVs and conventional local vias in 3D ICs has not been well investigated. This co-design is necessary when the die-to-die vertical power delivery is done using both TSVs and local interconnects. In this work, we model EM for PDNs of 3D ICs with a focus on multi-scale via (MSV) structure, i.e., TSVs and local vias used together for vertical power delivery. We study the impact of structure, material, and pre-existing void conditions on the EM-related lifetime of our multi-scale via structures. We also investigate the transient IR-voltage change of full-chip level 3D PDNs with MSVs with our model. The experimental results demonstrate that our EM modeling can effectively capture the EM reliability of the fullchip level 3D PDNs with MSVs, which can be hard to achieve by the traditional EM analysis based on the individual local via or the TSV.