Hydrolase that deubiquitinates monoubiquitinated target proteins such as histone H2A and H2B. Required for proper progression through S phase and subsequent mitotic entry. May regulate the DNA damage response (DDR) checkpoint through deubiquitination of H2A at DNA damage sites. Associates with the chromatin (By similarity). Thiol-dependent hydrolysis of ester, thioester, amide, peptide and isopeptide bonds formed by the C-terminal Gly of ubiquitin (a 76-residue protein attached to proteins as an intracellular targeting signal). Interacts (via UBP-type domain) with H2A; the interaction is less efficient than with monoubiquitinated H2A. Localizes preferentially with monoubiquitinated H2A to chromatin. Both protease activity and an intact zinc finger are required for H2A monodeubiquitination. Belongs to the peptidase C19 family. USP3 subfamily.