Background: Efficient decoding of motor imagery (MI) electroencephalogram (EEG) signals is essential for the precise control and practical deployment of brain-computer interface (BCI) systems. Owing to the complex nonlinear characteristics of EEG signals across spatial, spectral, and temporal dimensions, efficiently extracting multidimensional discriminative features remains a key challenge to improving MI-EEG decoding performance. Methods: To address the challenge of capturing complex spatial, spectral, and temporal features in MI-EEG signals, this study proposes a multi-branch deep neural network, which jointly models these dimensions to enhance classification performance. The network takes as inputs both a three-dimensional power spectral density tensor and two-dimensional time-domain EEG signals and incorporates four complementary feature extraction branches to capture spatial, spectral, spatial-spectral joint, and temporal dynamic features, thereby enabling unified multidimensional modeling. The model was comprehensively evaluated on two widely used public MI-EEG datasets: EEG Motor Movement/Imagery Database (EEGMMIDB) and BCI Competition IV Dataset 2a (BCIIV2A). To further assess interpretability, gradient-weighted class activation mapping (Grad-CAM) was employed to visualize the spatial and spectral features prioritized by the model. Results: On the EEGMMIDB dataset, it achieved an average classification accuracy of 86.34% and a kappa coefficient of 0.829 in the five-class task. On the BCIIV2A dataset, it reached an accuracy of 83.43% and a kappa coefficient of 0.779 in the four-class task. Conclusions: These results demonstrate that the network outperforms existing state-of-the-art methods in classification performance. Furthermore, Grad-CAM visualizations identified the key spatial channels and frequency bands attended to by the model, supporting its neurophysiological interpretability.