Catalyzes the cleavage of the N-glycosidic bond of deoxyribonucleoside 5'-monophosphates to yield deoxyribose 5-phosphate and a purine or pyrimidine base. a pyrimidine 2'-deoxyribonucleoside 5'-phosphate + H2O = 2-deoxy-D-ribose 5-phosphate + a pyrimidine nucleobase a purine 2'-deoxyribonucleoside 5'-phosphate + H2O = 2-deoxy-D-ribose 5-phosphate + a purine nucleobase Monomer and homodimer. Belongs to the 2'-deoxynucleoside 5'-phosphate N-hydrolase 1 family.