The Hi-C method is widely used to study the functional roles of the three-dimensional (3D) architecture of genomes. Here, we integrate Hi-C, whole-genome sequencing (WGS) and RNA-seq to study the 3D genome architecture of multiple myeloma (MM) and how it associates with genomic variation and gene expression. Our results show that Hi-C interaction matrices are biased by copy number variations (CNVs) and can be used to detect CNVs. Also, combining Hi-C and WGS data can improve the detection of translocations. We find that CNV breakpoints significantly overlap with topologically associating domain (TAD) boundaries. Compared to normal B cells, the numbers of TADs increases by 25% in MM, the average size of TADs is smaller, and about 20% of genomic regions switch their chromatin A/B compartment types. In summary, we report a 3D genome interaction map of aneuploid MM cells and reveal the relationship among CNVs, translocations, 3D genome reorganization, and gene expression regulation.