Published in: Phys. Rev., B 64 (2001) 024530 citations recorded in [Science Citation Index] Abstract: A detailed calculation is presented of the dielectric function in superconducttors consisting of two Josephson coupled superconducting layers per unit cell, taking into account the effect of finite compressibility of the electron fluid. From the model it follows, that two longitudinal, and one transverse optical Josephson plasma resonance exist in these materials, for electric field polarization perpendicular to the planes. The latter mode appears as a resonance in the transverse dielectric function, and it couples directly to the electrical field vector of infrared radiation. A shift of all plasma frequencies, and a reduction of the intensity of the transverse optical Josephson plasmon is shown to result from the finite compressibility of the electron fluid.