Mortar techniques provide a flexible tool for the coupling of different discretization schemes or triangulations. Here, we consider interface problems within the framework of mortar finite element methods. We start with a saddle point formulation and show that the interface conditions enter into the right-hand side. Using dual Lagrange multipliers, we can work with scaled sparse matrices, and static condensation gives rise to a symmetric and positive definite system on the unconstrained product space. The iterative solver is based on a modified multigrid approach. Numerical results illustrate the performance of our approach.