  We study Lie bialgebroid crossed modules which are pairs of Lie algebroid
crossed modules in duality that canonically give rise to Lie bialgebroids. A
one-one correspondence between such Lie bialgebroid crossed modules and
co-quadratic Manin triples $(K,P,Q)$ is established, where $K$ is a
co-quadratic Lie algebroid and $(P,Q)$ is a pair of transverse Dirac structures
in $K$.
