  We introduce the notion of Poisson superbialgebra as an analogue of
Drinfeld's Lie superbialgebras. We extend various known constructions dealing
with representations on Lie superbialgebras to Poisson superbialgebras. We
introduce the notions of Manin triple of Poisson superalgebras and Poisson
superbialgebras and show the equivalence between them in terms of matched pairs
of Poisson superalgebras. A combination of the classical Yang-Baxter equation
and the associative Yang-Baxter equation is discussed in this framework.
Moreover, we introduce notions of $\mathcal{O}$-operator of weight
$\lambda\in\mathbb{K}$ of a Poisson superalgebra and post-Poisson superalgebra
and interpret the close relationships between them and Poisson superbialgebras.
