In this paper, we consider multiple channels and wireless nodes with multiple transceivers. Each node assigns one transmitter at each available channel. For each assigned transmitter the node decides the power level and data rate of transmission in a distributed fashion, such that certain Quality of Service (QoS) demands for the wireless node are satisfied. More specifically, we investigate the case in which the average SINR over all channels for each communication pair is kept above a certain threshold. A joint distributed power and rate control algorithm for each transmitter is proposed that dynamically adjusts the data rate to meet a target SINR at each channel, and to update the power levels allowing for variable desired SINRs. The algorithm is fully distributed and requires only local interference measurements. The performance of the proposed algorithm is shown through illustrative examples.