In this paper we combine the dual-mixed finite element method with a Dirichlet-to-Neumann mapping
(given in terms of a boundary integral operator) to solve linear exterior transmission problems in
the plane. As a model we consider a second order elliptic equation in divergence form coupled with
the Laplace equation in the exterior unbounded region. We show that the resulting mixed variational
formulation and an associated discrete scheme using Raviart-Thomas spaces are well posed, and derive
the usual Cea error estimate and the corresponding rate of convergence. In addition, we develop two
different a-posteriori error analyses yielding explicit residual and implicit Bank-Weiser type
reliable estimates, respectively. Several numerical results illustrate the suitability of these
estimators for the adaptive computation of the discrete solutions.