In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates are independent of the precise discretization scheme and provide guaranteed upper bounds for the potential error. The computation of these upper bounds is based on the solutions of local auxiliary finite element problems on patches in the interior domain and in a strip domain along the coupling boundary. Numerical experiments illustrate the performance of the proposed error estimation strategy for a related adaptive mesh-refinement strategy.