  We derive a formula for the generating function of d-irreducible bipartite
planar maps with several boundaries, i.e. having several marked faces of
controlled degrees. It extends a formula due to Collet and Fusy for the case of
arbitrary (non necessarily irreducible) bipartite planar maps, which we recover
by taking d=0. As an application, we obtain an expression for the number of
d-irreducible bipartite planar maps with a prescribed number of faces of each
allowed degree. Very explicit expressions are given in the case of maps without
multiple edges (d=2), 4-irreducible maps and maps of girth at least 6 (d=4).
Our derivation is based on a tree interpretation of the various encountered
generating functions.
