It is common in anthropology and paleontology to address questions about extant and extinct species through the quantification of osteological features observable in micro-computed tomographic (mCT) scans. In cases where remains were buried, the grey values present in these scans may be classified as belonging to air, dirt, or bone. While various intensity-based methods have been proposed to segment scans into these classes, it is often the case that intensity values for dirt and bone are nearly indistinguishable. In these instances, scientists resort to laborious manual segmentation, which does not scale well in practice when a large number of scans are to be analyzed. Here we present a new domain-enriched network for three-class image segmentation, which utilizes the domain knowledge of experts familiar with manually segmenting bone and dirt structures. More precisely, our novel structure consists of two components: 1) a representation network trained on special samples based on newly designed custom loss terms, which extracts discriminative bone and dirt features, 2) and a segmentation network that leverages these extracted discriminative features. These two parts are jointly trained in order to optimize the segmentation performance. A comparison of our network to that of the current state-of-the-art U-NETs demonstrates the benefits of our proposal, particularly when the number of labeled training images are limited, which is invariably the case for mCT segmentation.