In this paper, we study an extended mixed Nite element method for dealing with elliptic interface problems. We propose a discrete mixed approximate form based on the Brezzi-Douglas-Marini Nite element space and a piecewise constant function space, and show thatthe inf-sup condition for the discrete problem is uniform with respect to the mesh size and the location of the interface relative to the mesh. Furthermore, we derive that the optimal convergence holds independent of the location of the interface relative to the mesh. Finally, some numerical examples are presented to demonstrate our theoretical results.