The sequences of homologous chromosomes differ in the presence of heterozygous single nucleotide polymorphisms (SNPs). Whether these differences translate into "heterozygous" chromatin three-dimensional structures is still largely unexplored. Here, we design HaploC-tools to optimize whole-chromosome phasing from high-throughput chromosome conformation capture (Hi-C) data and introduce tailored approaches to infer haplotype-specific copy number variants, boundary insulation, and chromatin compartmentalization. We use Haplo-C tools to analyze > 100 Hi-C dataset, including normal and cancer cell models, representing a unique resource to explore haplotype-specific chromatin conformation. Leveraging this dataset, we show that SNPs at CTCF binding sites lead to significantly different contact insulation between homologous chromosomes and discover widespread haplotype-specific compartments in cancer, driven by asymmetric loss of H3K9me3. These results implicate haplotype-specific chromatin configuration as a potential new mechanism of phenotypic reprogramming in disease emergence and progression.