The three-dimensional conformation of a genome can be profiled using Hi-C, a technique that combines chromatin conformation capture with high-throughput sequencing. However, structural variations often yield features that can be mistaken for chromosomal interactions. Here, we describe a computational method HiNT (Hi-C for copy Number variation and Translocation detection), which detects copy number variations and interchromosomal translocations within Hi-C data with breakpoints at single base-pair resolution. We demonstrate that HiNT outperforms existing methods on both simulated and real data. We also show that Hi-C can supplement whole-genome sequencing in structure variant detection by locating breakpoints in repetitive regions.