The relationships between chromosomal compartmentalization, chromatin state and function are poorly understood. Here by profiling long-range contact frequencies in HCT116 colon cancer cells, we distinguish three silent chromatin states, comprising two types of heterochromatin and a state enriched for H3K9me2 and H2A.Z that exhibits neutral three-dimensional interaction preferences and which, to our knowledge, has not previously been characterized. We find that heterochromatin marked by H3K9me3, HP1α and HP1β correlates with strong compartmentalization. We demonstrate that disruption of DNA methyltransferase activity greatly remodels genome compartmentalization whereby domains lose H3K9me3-HP1α/β binding and acquire the neutrally interacting state while retaining late replication timing. Furthermore, we show that H3K9me3-HP1α/β heterochromatin is permissive to loop extrusion by cohesin but refractory to CTCF binding. Together, our work reveals a dynamic structural and organizational diversity of the silent portion of the genome and establishes connections between the regulation of chromatin state and chromosome organization, including an interplay between DNA methylation, compartmentalization and loop extrusion.