  For a bounded Lipschitz domain with Lipschitz interface we show the following
compactness theorem: Any $L^2$-bounded sequence of vector fields with
$L^2$-bounded rotations and $L^2$-bounded divergences as well as $L^2$-bounded
tangential traces on one part of the boundary and $L^2$-bounded normal traces
on the other part of the boundary, contains a strongly $L^2$-convergent
subsequence. This generalises recent results for homogeneous mixed boundary
conditions by the first author and collaborators. As applications we present a
related Friedrichs/Poincare type estimate, a div-curl lemma, and show that the
Maxwell operator with mixed tangential and impedance boundary conditions (Robin
type boundary conditions) has compact resolvents.
