The three-dimensional (3D) imaging and quantitative analysis of bone microvasculature are important to describe angiogenesis involvement in bone metastatic processes. Here, we propose an algorithm based on marker controlled watershed for the 3D segmentation of vessels and bone in mouse bone imaged with a contrast agent using synchrotron radiation micro-computed tomography (SR-µCT). Markers were generated using hysteresis thresholding and morphological filters, and the control surface was constructed using the monogenic signal phase asymmetry. The accuracy and robustness of the proposed method were evaluated on a series of synthetic volumes generated to mimic the vessel, bone and background structures. Different contrast between different structures, as well as different noise levels were considered. A series of multi-class synthetic volumes were segmented using the proposed method, and the overall segmentation quality was evaluated using the Matthews correlation coefficient (MCC) by comparing to the ground truth. Additionally, we evaluated the segmentation of thin structures under various levels of Gaussian noise. The simulation study indicated that the algorithm was performant in multi-class segmentation with different contrast, noise, and thickness. The algorithm was applied to images of bone from a mouse model of breast cancer bone metastasis acquired using SR-µCT. The segmentation quality was evaluated using the Dice coefficient and the MCC by comparing to manual segmentation. The proposed method performed better than hysteresis thresholding and marker-controlled watershed using the magnitude of the gradient as control surface. Several quantitative parameters on bone and vessels were extracted. The bone volume fraction (BV/TV) was significantly lower in the metastatic group compared to the healthy group. There was no significant difference on the vessel volume fraction (VV/TV) and the vessel thickness (VTh), possibly due to the limited sample size. This demonstrated the effectiveness of the algorithm for the study of bone and vessel microstructures in mouse model.