We present a framework for automatically learning human user models from joint-action demonstrations that enables a robot to compute a robust policy for a collaborative task with a human. First, the demonstrated action sequences are clustered into different human types using an unsupervised learning algorithm. A reward function is then learned for each type through the employment of an inverse reinforcement learning algorithm. The learned model is then incorporated into a mixed-observability Markov decision process (MOMDP) formulation, wherein the human type is a partially observable variable. With this framework, we can infer online the human type of a new user that was not included in the training set, and can compute a policy for the robot that will be aligned to the preference of this user. In a human subject experiment (n = 30), participants agreed more strongly that the robot anticipated their actions when working with a robot incorporating the proposed framework (p < 0.01), compared to manually annotating robot actions. In trials where participants faced difficulty annotating the robot actions to complete the task, the proposed framework significantly improved team efficiency (p < 0.01). The robot incorporating the framework was also found to be more responsive to human actions compared to policies computed using a hand-coded reward function by a domain expert (p < 0.01). These results indicate that learning human user models from joint-action demonstrations and encoding them in a MOMDP formalism can support effective teaming in human-robot collaborative tasks.