The concept of a Lie bialgebroid, naturally arising in Poisson geometry, unifies the notions of Lie bialgebras and Lie algebroids. We give an interpretation of Lie bialgebroids and their morphisms in terms of odd symplectic differential graded manifolds using the Hamiltonian framework D.Roytenberg. Furthermore, this can be extended to the homotopy Lie case leading to the notions of homotopy Lie bialgebroids and morphisms between them.