We propose a 3D convolutional neural network to simultaneously segment and detect cell nuclei in confocal microscopy images. Mirroring the co-dependency of these tasks, our proposed model consists of two serial components: the first part computes a segmentation of cell bodies, while the second module identifies the centers of these cells. Our model is trained end-to-end from scratch on a mouse parotid salivary gland stem cell nuclei dataset comprising 107 3D images from three independent cell preparations, each containing several hundred individual cell nuclei in 3D. In our experiments, we conduct a thorough evaluation of both detection accuracy and segmentation quality, on two different datasets. The results show that the proposed method provides significantly improved detection and segmentation accuracy compared to existing algorithms. Finally, we use a previously described test-time drop-out strategy to obtain uncertainty estimates on our predictions and validate these estimates by demonstrating that they are strongly correlated with accuracy.