Cohesin plays an essential role in chromatin loop extrusion, but its impact on a compartmentalized nuclear architecture, linked to nuclear functions, is less well understood. Using live-cell and super-resolved 3D microscopy, here we find that cohesin depletion in a human colon cancer derived cell line results in endomitosis and a single multilobulated nucleus with chromosome territories pervaded by interchromatin channels. Chromosome territories contain chromatin domain clusters with a zonal organization of repressed chromatin domains in the interior and transcriptionally competent domains located at the periphery. These clusters form microscopically defined, active and inactive compartments, which likely correspond to A/B compartments, which are detected with ensemble Hi-C. Splicing speckles are observed nearby within the lining channel system. We further observe that the multilobulated nuclei, despite continuous absence of cohesin, pass through S-phase with typical spatio-temporal patterns of replication domains. Evidence for structural changes of these domains compared to controls suggests that cohesin is required for their full integrity.