We prove the well-posedness and stability properties of a parameter dependent problem that models the reflection and transmission of electromagnetic waves at a thin and rapidly oscillating interface. The latter is modeled using approximate interface conditions that can be derived using asymptotic expansion of the exact solution with respect to the small parameter (proportional to the periodicity length of oscillations and the width of the interface). The obtained uniform stability results are then used to prove the accuracy (with respect to the small parameter) of the proposed model.