Mammalian genomes are organized into three-dimensional DNA structures called A/B compartments that are associated with transcriptional activity/inactivity. However, whether these structures are simply correlated with gene expression or are permissive/impermissible to transcription has remained largely unknown because we lack methods to measure DNA organization and transcription simultaneously. Recently, we developed RNA & DNA (RD)-SPRITE, which enables genome-wide measurements of the spatial organization of RNA and DNA. Here we show that RD-SPRITE measures genomic structure surrounding nascent pre-mRNAs and maps their spatial contacts. We find that transcription occurs within B compartments—with multiple active genes simultaneously colocalizing within the same B compartment—and at genes proximal to nucleoli. These results suggest that localization near or within nuclear structures thought to be inactive does not preclude transcription and that active transcription can occur throughout the nucleus. In general, we anticipate RD-SPRITE will be a powerful tool for exploring relationships between genome structure and transcription. Display omitted •RD-SPRITE enables simultaneous mapping of nascent transcription and DNA structure•Pol II transcription occurs within both A and B compartments and proximal to nucleoli•Nascent pre-mRNAs organize within chromosome territories and A/B compartments•Our findings argue against structural domains that preclude RNA Pol II transcription Using RD-SPRITE to simultaneously map 3D genome structure and nascent RNA transcription genome-wide, Goronzy et al. find that RNA polymerase II transcription can occur within multiple compartments in the nucleus, including regions previously associated with inactive transcription, such as the B compartment and close to the nucleolus.