  We consider three different methods for the coupling of the finite element
method and the boundary element method, the Bielak-MacCamy coupling, the
symmetric coupling, and the Johnson-N\'ed\'elec coupling. For each coupling we
provide discrete interior regularity estimates. As a consequence, we are able
to prove the existence of exponentially convergent $\mathcal{H}$-matrix
approximants to the inverse matrices corresponding to the lowest order Galerkin
discretizations of the couplings.
