Dual specificity phosphatase that dephosphorylates MAPK8/JNK and MAPK14/p38, but not MAPK1/ERK2, in vitro (PubMed:21360282). Exhibits intrinsic phosphatase activity towards both phospho- seryl/threonyl and -tyrosyl residues, with similar specific activities in vitro (PubMed:10585869). {ECO:0000269|PubMed:10585869, ECO:0000269|PubMed:21360282}. This is the function of DUSP13B (dual specificity phosphatase 13B, Ensembl gene identifier ENSG00000079393).