Three-dimensional (3D) audio technologies are booming with the success of 3D video technology. The surge in audio channels makes its huge data unacceptable for transmitting bandwidth and storage media, and the signal compression algorithm for 3D audio systems becomes an important task. This paper investigates the conventional mid/side (M/S) coding method and discusses the signal correlation property of three-dimensional multichannel systems. Then based on the channel triple, a three-channel dependent M/S coding (3D-M/S) method is proposed to reduce interchannel redundancy and corresponding transform matrices are presented. Furthermore, a framework is proposed to enable 3D-M/S compress any number of audio channels. Finally, the masking threshold of the perceptual audio core codec is modified, which guarantees the final coding noise to meet the perceptual threshold constraint of the original channel signals. Objective and subjective tests with panning signals indicate an increase in coding efficiency compared to Independent channel coding and a moderate complexity increase compared to a PCA method.