  We study the equivalence between the $B\wedge F$ self-dual ($SD_{B\wedge F}$)
and the $B\wedge F$ topologically massive ($TM_{B\wedge F}$) models including
the coupling to dynamical, U(1) charged fermionic matter. This is done through
an iterative procedure of gauge embedding that produces the dual mapping. In
the interactive cases, the minimal coupling adopted for both vector and tensor
fields in the self-dual representation is transformed into a non minimal
magnetic like coupling in the topologically massive representation but with the
currents swapped. It is known that to establish this equivalence a
current-current interaction term is needed to render the matter sector
unchanged. We show that both terms arise naturally from the embedding
procedure.
