A transverse optical plasma mode is observed at far-infrared frequencies within the superconducting gap region by measuring the c-axis optical reflectivity for single crystals of T* cuprate superconductors SmLa0.85Sr0.15CuO4-delta and Nd1.4Sr0.4Ce0.2CuO4-delta. These T* cuprates have two different insulating layers sandwiching the superconducting CuO2 planes, leading to two longitudinal plasmons. Also, the transverse mode is directly observed due to the coupling of the infrared radiation with the current perpendicular to the superconducting layers which are regarded as an alternating array of two inequivalent Josephson junctions.