Accurate segmentation of cellular structures is critical for automating the analysis of microscopy data. Advances in deep learning have facilitated extensive improvements in semantic image segmentation. In particular, U-Net, a model specifically developed for biomedical image data, performs multi-instance segmentation through pixel-based classification. However, approaches based on U-Net tend to merge touching cells in dense cell cultures, resulting in under-segmentation. To address this issue, we propose DeepSplit; a multi-task convolutional neural network architecture where one encoding path splits into two decoding branches. DeepSplit first learns segmentation masks, then explicitly learns the more challenging cell-cell contact regions. We test our approach on a challenging dataset of cells that are highly variable in terms of shape and intensity. DeepSplit achieves 90% cell detection coefficient and 90% Dice Similarity Coefficient (DSC) which is a significant improvement on the state-of-the-art U-Net that scored 70% and 84% respectively.