Gearbox fault diagnosis plays a pivotal role in the implementation of predictive maintenance and minimizing the economic losses caused by unexpected equipment failures. Due to the variable-speed operating conditions in gear transmission systems, the collected vibration signals often exhibit intricate amplitude and frequency modulation characteristics. Accurately extracting the hidden fault information requires considerable expertise from maintenance engineers. To overcome the aforementioned limitations of conventional diagnostic methods, this paper proposes a fault diagnosis method for planetary gearboxes based on dual-stream deep residual network, which extracts the modulation features using Modulation Signal Bispectrum (MSB). Since the gear fault signatures are typically extracted from the modulation information, the proposed method applies a MSB algorithm to obtain the nonlinear modulation features of the vibration signals. A dual-stream ResNet model is designed to perform joint learning on the obtained magnitudes and coherence for effective fault classification. The classification accuracy and generalization capability of the proposed diagnostic method are validated using experimental datasets of planetary gearbox faults. The diagnostic performance of the developed method surpasses that of conventional convolution neural network (CNN), offering a reliable and effective solution for condition monitoring of planetary gearboxes.