Genomic characterization has revealed widespread structural complexity in cancer karyotypes, however shotgun sequencing cannot resolve genomic rearrangements with chromosome-length continuity. Here, we describe a two-tiered approach to determine the segmental composition of rearranged chromosomes with haplotype resolution. First, we present refLinker , a new method for robust determination of chromosomal haplotypes using cancer Hi-C data. Second, we use haplotype-specific Hi-C contacts to determine the segmental structure of rearranged chromosomes. By contrast with existing methods for diploid haplotype inference, our approach is robust to the confounding effects of large-scale DNA deletions, duplications, and high-level amplification in cancer sequencing. Using this approach, we examine haplotype-specific expression changes on rearranged homologs and provide direct evidence for long-range transcriptional activation and repression associated with rearrangements of the inactive X chromosome (Xi). Together, these results reveal the significant transcriptional consequences of somatic Xi rearrangements, highlighting refLinker 's broad utility for studying the functional consequences of chromosomal rearrangements.