As one of the most important research fields in the brain-computer interface (BCI) field, electroencephalogram (EEG) classification has a wide range of application values. However, for the EEG signal, it is difficult for the traditional neural networks to capture the characteristics of the EEG signal more comprehensively from the time and space dimensions, which has a certain effect on the accuracy of EEG classification. To solve this problem, we can improve the accuracy of classification via end-to-end learning of the time and space dimensions of EEG. In this paper, a new type of EEG classification network, the separable EEGNet (S-EEGNet), is proposed based on Hilbert-Huang transform (HHT) and a separable convolutional neural network (CNN) with bilinear interpolation. The EEG signal is transformed into time-frequency representation by HHT, which allows the EEG signal to be better described in the frequency domain. Then, the depthwise and pointwise elements of the network are combined to extract the feature map. The displacement variable is added by the bilinear interpolation method to the convolution layer of the separable CNN, allowing the free deformation of the sampling grid. The deformation depends on the local, dense, and adaptive input characteristics of the EEG data. The network can learn from the time and space dimensions of EEG signals end to end to extract features to improve the accuracy of EEG classification. To show the effectiveness of S-EEGNet, the team used this method to test two different types of EEG public datasets (motor imagery classification and emotion classification). The accuracy of motor imagery classification is 77.9%, and the accuracy of emotion classification is 89.91%, and 88.31%, respectively. The experimental results showed that the classification accuracy of S-EEGNet improved by 3.6%, 1.15%, and 1.33%, respectively.