  We derive the complete set of off-shell nilpotent and absolutely
anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry
transformations corresponding to the combined "scalar" and "vector" gauge
symmetry transformations for the (3+1)-dimensional (4D) topologically massive
non-Abelian $(B \wedge F)$ theory with the help of geometrical superfield
formalism. For this purpose, we use three horizontality conditions (HCs). The
first HC produces the (anti-)BRST transformations for the 1-form gauge field
and corresponding (anti-)ghost fields whereas the second HC yields the
(anti-)BRST transformations for 2-form field and associated (anti-)ghost
fields. The integrability of second HC produces third HC. The latter HC
produces the (anti-)BRST symmetry transformations for the compensating
auxiliary vector field and corresponding ghosts. We obtain five (anti-)BRST
invariant Curci-Ferrari (CF)-type conditions which emerge very naturally as the
off-shoots of superfield formalism. Out of five CF-type conditions, two are
fermionic in nature. These CF-type conditions play a decisive role in providing
the absolute anticommutativity of the (anti-)BRST transformations and also
responsible for the derivation of coupled but equivalent (anti-)BRST invariant
Lagrangian densities. Furthermore, we capture the (anti-)BRST invariance of the
coupled Lagrangian densities in terms of the superfields and translation
generators along the Grassmannian directions $\theta$ and $\bar \theta$.
