Multi-target tracking in various security, surveillance, and reconnaissance tasks involves a large number of moving targets moving around in large workspaces motivating the use of mobile, distributed, and cooperative robot swarms. Incorporating human operators in these multi-robot multi-target tracking tasks can make the robot swarms more adaptive, increase robustness and scalability, and hence improve the overall tracking performance. However, collaboration in these mixed human-robot teams (MHRTs) raises concerns about how to enable communication between the human operator and the robot swarm, and how to design robot planning and control algorithms that efficiently leverage information from the human operator. This paper presents a cooperative tracking framework for multi-robot multi-target tracking. A novel mixed-initiative cooperation strategy to facilitate communication between the human and robots is presented. A new tracking utility function is developed to incorporate human inputs and enable a distributed robot network equipped with directional field-of-view (FOV) sensors to track multiple moving targets simultaneously in obstacle-populated environments. An online target state estimation framework is developed to leverage learning-based perception algorithms for target detection, classification, and estimation for tracking. This target state estimation framework is used to test the cooperative tracking framework with a team of ground robots equipped with RGBD cameras. Using simulation studies and physical experiments it is shown that this framework can provide robust performance in the presence of uncertainties such as state estimation errors and intruders and consistently outperform homogeneous robot teams.