The study of mouse social behaviors has been increasingly undertaken in neuroscience research. However, automated quantification of mouse behaviors from the videos of interacting mice is still a challenging problem, where object tracking plays a key role in locating mice in their living spaces. Artificial markers are often applied for multiple mice tracking, which are intrusive and consequently interfere with the movements of mice in a dynamic environment. In this article, we propose a novel method to continuously track several mice and individual parts without requiring any specific tagging. First, we propose an efficient and robust deep-learning-based mouse part detection scheme to generate part candidates. Subsequently, we propose a novel Bayesian-inference integer linear programming (BILP) model that jointly assigns the part candidates to individual targets with necessary geometric constraints while establishing pair-wise association between the detected parts. There is no publicly available dataset in the research community that provides a quantitative test bed for part detection and tracking of multiple mice, and we here introduce a new challenging Multi-Mice PartsTrack dataset that is made of complex behaviors. Finally, we evaluate our proposed approach against several baselines on our new datasets, where the results show that our method outperforms the other state-of-the-art approaches in terms of accuracy. We also demonstrate the generalization ability of the proposed approach on tracking zebra and locust.