  Li-Bland's correspondence between linear Courant algebroids and Lie
$2$-algebroids is explained and shown to be an equivalence of categories.
Decomposed VB-Courant algebroids are shown to be equivalent to split Lie
2-algebroids in the same manner as decomposed VB-algebroids are equivalent to
2-term representations up to homotopy (Gracia-Saz and Mehta). Several classes
of examples are discussed, yielding new examples of split Lie 2-algebroids. We
prove that the bicrossproduct of a matched pair of $2$-representations is a
split Lie $2$-algebroid and we explain this result geometrically, as a
consequence of the equivalence of VB-Courant algebroids and Lie $2$-algebroids.
This explains in particular how the two notions of double" of a matched pair of
representations are geometrically related. In the same manner, we explain the
geometric link between the two notions of double of a Lie bialgebroid.
