We consider a simplified scalar model problem related to Maxwell equations, involving wave transmission between media with opposite sign dielectric constant. We build two variational formulations equivalent to model problem. We show that, under some suitable conditions, every formulation is well posed since it fits into the coercive plus compact framework. Advantages over previous studies is the validity of the formulations in the general case of Lipschitz interface between the two media and $L^\infty$ dielectric constant. Moreover the three-field formulation allows to handle a more general set of equations. A main interest of these formulations is that they allow a simple finite element numerical treatement.