The transmission and reflection properties of a meta-stack composed of a periodic AB arrangement of an air(A)/metamaterial(B) bilayer is presented, with the multi layered system embedded between two semi-infinite layers of the A material. For oblique incidence, a finite projection along the growth direction of the electric or magnetic field of the incident wave associated with the TM or TE modes, respectively, leads to a coupling of the photon modes with the bulk electric or magnetic metamaterial plasmons, in each layer of the meta-stack. This field-matter coupling gives rise to plasmon-polariton modes and signatures of electric or magnetic longitudinal bulk-plasmon polariton modes in the transmission, as well as in the reflection properties of the meta-stack, by means of a plasmon-polariton gap. Such features survive even in the case of a single bilayer and experimental observation should be, therefore, easily achieved.