  We analyze a multilevel diagonal additive Schwarz preconditioner for the
adaptive coupling of FEM and BEM for a linear 2D Laplace transmission problem.
We rigorously prove that the condition number of the preconditioned system
stays uniformly bounded, independently of the refinement level and the local
mesh-size of the underlying adaptively refined triangulations. Although the
focus is on the non-symmetric Johnson-N\'ed\'elec one-equation coupling, the
principle ideas also apply to other formulations like the symmetric FEM-BEM
coupling. Numerical experiments underline our theoretical findings.
