Large portions of mammalian genomes are packaged into structurally compact heterochromatin, which protects genome integrity and suppresses transcription of lineage-inappropriate genes. Characterization of heterochromatic regions has relied on genomic mapping of associated histone modifications, such as H3K9me3 and H3K27me3, and purification of proteins interacting with these modifications. Heterochromatic regions marked by H3K9me3 have been shown to impede gene activation during reprogramming to pluripotency, and I find that H3K9me3 domains can similarly impede conversion of fibroblasts to hepatocytes. However, both H3K9me3 and H3K27me3 can be found in transcriptionally active chromatin, limiting the accuracy of histone marks alone for identifying heterochromatin domains or bound proteins that impede reprogramming. I developed a biophysical method to purify heterochromatic regions, using sucrose gradients to isolate chromatin fragments that are resistant to sonication. Sequencing of the purified material (Gradient-seq) revealed the genomic landscape of structural heterochromatin in human fibroblasts, which is transcribed at low levels and contains largely distinct H3K9me3 and H3K27me3 domains, as well as unmarked regions. Gradient-seq also uncovered subtypes of H3K9me3 and H3K27me3 domains that are structurally euchromatic, a distinction corroborated by increased gene transcription, hypomethylation at CpG islands, decreased association with the nuclear lamina, and increased activation during hepatic reprogramming. Using quantitative proteomics, we found 172 proteins associated with heterochromatin after gradient sedimentation and H3K9me3-directed IP. The identified proteins include known transcriptional repressors and are enriched for proteins shown to impede reprogramming to pluripotency. We show that the RNA-binding protein RBMX, one of the proteins most enriched by gradient sedimentation and H3K9me3 IP, is a functional regulator of heterochromatin. RBMX and the related protein RBMXL1 are required for silencing of select heterochromatinized genes, and depletion of these proteins in fibroblasts renders H3K9me3-marked hepatocyte genes more competent for activation during reprogramming to the hepatic lineage. Thus, our biophysical method for heterochromatin isolation has allowed us to create a genome-wide map of chromatin compaction in human cells, to identify chromatin domain subtypes that impede conversion between differentiated lineages, and to discover novel heterochromatin proteins that contribute to this reprogramming barrier.