We introduce hyperoctahedral species ($\H$-species) or species of type B, which are analogous to the classical tensor species, but on which we consider the action of the groups of signed permutations. We give a bistrong monoidal functor, a functor which preserves Hopf monoids, between the monoidal categories of species and H-species. We also define bilax monoidal functors (functors which preserve the structure of bimonoids) between the category of H-species and the category of graded vector spaces. Using these functors, the combinatorial Hopf algebra DQSym is shown to arise from the cofree comonoid on the exponential species.