This letter presents the scattering and tunneling properties of multilayered periodic arrangement composed of frequency selective surfaces (FSS). Each surface is composed of a linear array of cylindrical metallodielectric posts. This arrangement constitutes a two-dimensional (2-D) electromagnetic band gap (EBG) structure. The electromagnetic curtain effect, realized by a rotation of the scatterers in the structure under investigation, is discussed in this letter. The effect of complete wave tunneling, which was previously observed in a structure composed of a pair of epsilon-negative and mu-negative medium, and also in a pair of different FSS stacks characterized by dual behaviors, is also discussed here for the wave propagating through the proposed structure.