  In this paper we compute the bivariate generating function of
$\gamma$-matchings over two backbones, filtered by the number of arcs and the
topological genus. $\gamma$-matchings over two backbones are chord-diagrams,
obtained via concatenation and nesting of irreducible shapes of topological
genus $\le \gamma$. We show that the key information is contained in the
polynomials counting these shapes and provide recursions that allow to compute
the latter. In particular we give a bijection between such irreducible shapes
over one and two backbones. We present two applications of our results. The
first is concerned with RNA-RNA interaction structures, obtained from the
$\gamma$-matchings via symbolic methods. We secondly show that, using
analytic-combinatorial methods, the topological genus satisfies a central limit
theorem.
