A variety of genetic mutations affect cell proliferation during organism development, leading to structural birth defects. However, the mechanisms by which these alterations influence the development of the face remain unclear. Cell proliferation and its relation to shape variation can be studied using Light-Sheet Microscopy (LSM) imaging across a range of developmental time points using mouse models. The aim of this work was to develop and evaluate accurate automatic methods based on convolutional neural networks (CNNs) for: (i) tissue segmentation (neural ectoderm and mesenchyme), (ii) cell segmentation in nuclear-stained images, and (iii) segmentation of proliferating cells in phospho-Histone H3 (pHH3)-stained LSM images of mouse embryos. For training and evaluation of the CNN models, 155 to 176 slices from 10 mouse embryo LSM images with corresponding manual segmentations were available depending on the segmentation task. Three U-net CNN models were trained optimizing their loss functions, among other hyper-parameters, depending on the segmentation task. The tissue segmentation achieved a macro-average F-score of 0.84, whereas the inter-observer value was 0.89. The cell segmentation achieved a Dice score of 0.57 and 0.56 for nuclear-stained and pHH3-stained images, respectively, whereas the corresponding inter-observer Dice scores were 0.39 and 0.45, respectively. The proposed pipeline using the U-net CNN architecture can accelerate LSM image analysis and together with the annotated datasets can serve as a reference for comparison of more advanced LSM image segmentation methods in future.