Automatic nuclei segmentation and classification plays an important role in histopathological image analysis. However, existing algorithms mainly targeting H&E images have not provided a satisfied performance in processing immunohistochemical (IHC) images. On this account, we propose a multi-task deep learning model termed as the SRSA-Net to simultaneously segment and classify cell nuclei in IHC images. The SRSA-Net adopts ResNet50 augmented depth-wise separable convolution within each ResUnit as the feature encoder. Three paralleled decoder branches consist of self-attention modules and a series of DenseUnit and upsampling operations to derive results of nuclei classification, distance map prediction and nuclei segmentation. The watershed algorithm is finally used as a post-processing step to split touching cell nuclei. Experiments have been performed on the IHC dataset with more than 9000 cell nuclei, which show that the proposed SRSA-Net outperforms state-of-the-art nuclei segmentation and classification models.