  We discuss the complete sets of the off-shell nilpotent (i.e. s^2_{(a)b} = 0)
and absolutely anticommuting (i.e. s_b s_{ab} + s_{ab} s_b = 0)
Becchi-Rouet-Stora-Tyutin (BRST) (s_b) and anti-BRST (s_{ab}) symmetries for
the (3+1)-dimensional (4D) gauge-invariant massive 2-form theory within the
framework of augmented superfield approach to BRST formalism. In this
formalism, we obtain the coupled (but equivalent) Lagrangian densities which
respect both BRST and anti-BRST symmetries on the constrained hypersurface
defined by the Curci-Ferrari type conditions. The absolute anticommutativity
property of the (anti-)BRST transformations (and corresponding generators) is
ensured by the existence of the Curci-Ferrari type conditions which emerge very
naturally in this formalism. Furthermore, the gauge-invariant restriction plays
a decisive role in deriving the proper (anti-)BRST transformations for the
St{\"u}ckelberg-like vector field.
