Chromosomes must correctly fold in eukaryotic nuclei for proper genome function. Eukaryotic organisms hierarchically organize their genomes: in the fungus Neurospora crassa, chromatin fiber loops compact into Topologically Associated Domain (TAD)-like structures that are anchored by the aggregation of silent heterochromatic regions. However, insufficient information exists on how histone post-translational modifications, including acetylation, impact genome organization. In Neurospora, the HCHC complex (comprised of the proteins HDA-1, CDP-2, HP1, CHAP) deacetylates heterochromatic regions, including centromeres: loss of individual HCHC members increases centromeric acetylation and cytosine methylation. Here, we evaluate the role of the HCHC complex on genome organization using chromosome conformation capture with high-throughput sequencing (Hi-C) in strains deleted of the cdp-2 or chap genes. CDP-2 loss increases interactions between intra- and inter-chromosomal heterochromatic regions, while CHAP deletion decreases heterochromatic region compaction. Individual HCHC mutants exhibit different histone PTM patterns genome-wide: without CDP-2, heterochromatic H4K16 acetylation is increased, yet some heterochromatic regions lose H3K9 trimethylation, which increases interactions between heterochromatic regions; CHAP loss produces minimal acetylation changes but increases H3K9me3 enrichment in heterochromatin. Interestingly, deletion of the gene encoding the DIM-2 DNA methyltransferase in a cdp-2 deletion background causes extensive genome disorder, as heterochromatic-euchromatic contacts increase despite additional H3K9me3 enrichment. Our results highlight how the increased cytosine methylation in HCHC mutants ensures heterochromatic compartmentalization when silenced regions are hyperacetylated.