Inductive coupling is commonly used for wireless power and data transfer in biomedical telemetry systems. To increase data bandwidth while maintaining power transfer efficiency, a multiband telemetry system transmitting power and data using different frequencies has been adopted. However, the power link and data link interact with each other, complicating the operation of both power and data transmission. In this paper, we demonstrate that to achieve high performance data transmission, the cross-coupling between the power coils and data coils have to be taken into consideration. Design equations have been derived and shown that the signal to noise (interference) ratio could be significantly reduced and the resulting data transmission could fail if only the data link coupling is optimized without considering the cross-coupling between the power link and the data link. Design examples have been constructed to demonstrate that there could be more than 30 dB difference in the signal to noise ratio. The analysis has been verified with simulation and measurement results.