Bifunctional mitochondrial folate-interconverting enzyme that has both NAD/NADP-dependent methylenetetrahydrofolate dehydrogenase and methenyltetrahydrofolate cyclohydrolase activities. Has no NAD/NADP-dependent methylenetetrahydrofolate dehydrogenase activity. (6R)-5,10-methylene-5,6,7,8-tetrahydrofolate + NADP(+) = 5,10-methenyltetrahydrofolate + NADPH (6R)-5,10-methylene-5,6,7,8-tetrahydrofolate + NAD(+) = 5,10-methenyltetrahydrofolate + NADH 5,10-methenyltetrahydrofolate + H2O = (6S)-10-formyltetrahydrofolate + H(+) Has similar catalytic efficiencies, at physiological concentrations, with either NAD(+) or NADP(+) as substrates for the dehydrogenation of (6R)-5,10-methylene-5,6,7,8-tetrahydrofolate. One-carbon metabolism; tetrahydrofolate interconversion. Widely expressed. Belongs to the tetrahydrofolate dehydrogenase/cyclohydrolase family.