Chromosome conformation capture methods, such as Hi-C, have been used to profile chromosome organization from a wide variety of biosamples and conditions; however, existing methods for analyzing such datasets have disadvantages for large-scale integrative studies of long-range interactions. To address this shortcoming, we introduce an analytical framework, jointly-hic, that computes harmonized projections across arbitrarily many contact frequency matrices, suitable for integrative studies of compartmentalization and long-range interactions. Our approach produces robust and directly comparable first and higher-order principal component scores that collectively capture biologically meaningful information beyond traditional A/B compartment scores.