Cortical bone microstructure assessment in biological and forensic anthropology can assist with the estimation of age-at-death and animal-human differentiation, for example. Osteonal structures within cortical bone are the key feature under analysis, with osteon frequency and metric parameters providing crucial information for the assessment. Currently, the histomorphological assessment consists of a time-consuming manual process for which specific training is required. Our work investigates the feasibility of automatic analysis of human bone microstructure images through the application of deep learning. In this paper, we use a U-Net architecture to address the semantic segmentation of such images into three classes: intact osteons, fragmentary osteons, and background. Data augmentation was used to avoid overfitting. We evaluated our fully automatic approach using a sample of 99 microphotographs. The contours of intact and fragmentary osteons were traced manually to provide ground truth. The Dice coefficients were 0.73 for intact osteons, 0.38 for fragmented osteons, and 0.81 for background, giving an average of 0.64. The Dice coefficient of the binary classification osteon-background was 0.82. Although further refinement of the initial model and tests with larger datasets are needed, this study provides, to the best of our knowledge, the first proof of concept for the use of computer vision and deep learning for differentiating both intact and fragmentary osteons in human cortical bone. This approach has the potential to widen and facilitate the use of histomorphological assessment in the biological and forensic anthropology communities.