Diploid human cells contain two non-identical genomes, and differences in their regulation underlie human development and disease. We present Fiber-seq Inferred Regulatory Elements (FIRE) and show that FIRE provides a more comprehensive and quantitative snapshot of the accessible chromatin landscape across the 6 Gbp diploid human genome, overcoming previously unrecognized biases in existing regulatory element catalogs. FIRE enables comprehensive detection of haplotype-selective chromatin accessibility (HSCA), exposing novel imprinted elements lacking underlying parent-of-origin CpG methylation differences, and gene regulatory modules that permit genes to escape X chromosome inactivation. We uncover that the human leukocyte antigen (HLA) locus harbors the most HSCA in immune cells, where we resolve specific transcription factor (TF) binding events disrupted by disease-associated variants. Finally, we demonstrate that the regulatory landscape of a cell is littered with autosomal somatic chromatin epimutations that are propagated by clonal expansions to create mitotically stable and non-genetically deterministic chromatin alterations.