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In this paper, we present the theoretical study of ring-bus-ring coupled into Mach-Zehnder interferometer (RBR-MZI) device, which is capable of generating transparent window analogy to the electromagnetically induced transparency (EIT) phenomenon in atomic system. The RBR is a new class of two-resonator system, where the inter-cavity interaction is facilitated by a tri-coupler, instead of conventional coupler in other two-resonator systems. When the two rings are slightly detuned from one another, it is possible to obtain EIT-like transparent resonance when the RBR is integrated into MZI device. Good agreement is obtained between the analytical formulations and 2D-FDTD numerical simulations.