Biomedical implanted electronic devices utilize inductively coupled coils for power and data transmission. To achieve efficient power transmission and high data rate, a dual band telemetry system has been proposed where different carrier frequencies can be used for power and data transmission, respectively. In this system, the physical parameters and geometrical structure of the coils must be carefully optimized to avoid the strong power interference to data transmission, which diminishes the advantages of multiple carrier frequencies. In this demonstration, an optimization procedure is introduced about the optimization of two pairs of coils based on an overlapping structure which minimizes power-to-signal interference in the data transmission. We applied the optimization procedure to a practical design case, and the results showed that our optimization procedure can achieve both optimal power transmission efficiency and high signal to interference ratio.