The dynamically organized chromatin complexes often involve multiplex chromatin interactions and sometimes chromatin-associated RNA (caRNA) 1-3. Chromatin complex compositions change during cellular differentiation and aging, and are expected to be highly heterogeneous among terminally differentiated single cells 4-7. Here we introduce the Multi-Nucleic Acid Interaction Mapping in Single Cell (MUSIC) technique for concurrent profiling of multiplex chromatin interactions, gene expression, and RNA-chromatin associations within individual nuclei. Applied to 14 human frontal cortex samples from elderly donors, MUSIC delineates diverse cortical cell types and states. We observed the nuclei exhibiting fewer short-range chromatin interactions are correlated with an "older" transcriptomic signature and with Alzheimer's pathology. Furthermore, the cell type exhibiting chromatin contacts between cis expression quantitative trait loci (cis eQTLs) and a promoter tends to be the cell type where these cis eQTLs specifically affect their target gene's expression. Additionally, the female cortical cells exhibit highly heterogeneous interactions between the XIST non-coding RNA and Chromosome X, along with diverse spatial organizations of the X chromosomes. MUSIC presents a potent tool for exploring chromatin architecture and transcription at cellular resolution in complex tissues.