The temporal coupled-mode theory (TCMT) for a ring-bus-ring Mach-Zehnder interferometer device is developed by taking energy conservation into account. The intercavity interaction in the device is facilitated via a tricoupler, which makes the decay of modes quantitatively different from that in other existing resonator schemes. The TCMT is related to the transfer matrix formalism with energy conservation and the Q factor, and it predicts results in good agreement with the experimental results. The mode analysis from the TCMT is quite illustrative because it can mimic the transparency as an electromagnetically induced transparency expression. The analysis of the tricoupler is applicable for analyzing the transparent resonance in two other similar configurations.