We study the mixed human-robot team design in a system theoretic setting using the context of a surveillance mission. The three key coupled components of a mixed team design are (i) policies for the human operator, (ii) policies to account for erroneous human decisions, and (iii) policies to control the automaton. In this paper, we survey elements of human decision-making, including evidence aggregation, situational awareness, fatigue, and memory effects. We bring together the models for these elements in human decision-making to develop a single coherent model for human decision-making in a two-alternative choice task. We utilize the developed model to design efficient attention allocation policies for the human operator. We propose an anomaly detection algorithm that utilizes potentially erroneous decision by the operator to ascertain an anomalous region among the set of regions surveilled. Finally, we propose a stochastic vehicle routing policy that surveils an anomalous region with high probability. Our mixed team design relies on the certainty-equivalent receding-horizon control framework.