Image segmentation plays a crucial role in target recognition as it provides an essential prerequisite for identifying targets. However, UNet cannot acquire comprehensive information about the image, which limits its ability to effectively segment small and discrete objects. A new network structure, called MorNet, is proposed. It applies dilation and erosion operations in morphological opening and closing for connected and discrete region segmentation. MorNet effectively integrates global segmentation images, emphasizing small and discrete area segmentation and enhancing the segmentation of large continuous areas. This method enhances the understanding of the location of organs and diseased sites, enabling accurate segmentation. A side-out (SO) monitoring mechanism is introduced into the decoder to provide monitoring information for the original image and the predicted results. Compared with current UNet-like networks, our proposed method achieved the highest Dice scores (96.4635%, 94.0514%, 94.3444%) and PPV scores (94.2226%, 90.2361%, 91.5582%) for liver tumor, brain tumor, and liver segmentation tasks, respectively. The experimental results show that MorNet successfully combines the segmentation of connected and discrete regions. MorNet locates organs and lesions more accurately than current state-of-the-art medical image segmentation models.