The design of human–robot interactions is a key challenge to optimize operational performance. A promising approach is to consider mixed-initiative interactions in which the tasks and authority of each human and artificial agents are dynamically defined according to their current abilities. An important issue for the implementation of mixed-initiative systems is to monitor human performance to dynamically drive task allocation between human and artificial agents (i.e., robots). We, therefore, designed an experimental scenario involving missions whereby participants had to cooperate with a robot to fight fires while facing hazards. Two levels of robot automation (manual vs. autonomous) were randomly manipulated to assess their impact on the participants’ performance across missions. Cardiac activity, eye-tracking, and participants’ actions on the user interface were collected. The participants performed differently to an extent that we could identify high and low score mission groups that also exhibited different behavioral, cardiac and ocular patterns. More specifically, our findings indicated that the higher level of automation could be beneficial to low-scoring participants but detrimental to high-scoring ones, and vice versa. In addition, inter-subject single-trial classification results showed that the studied behavioral and physiological features were relevant to predict mission performance. The highest average balanced accuracy (74%) was reached using the features extracted from all input devices. These results suggest that an adaptive HRI driving system, that would aim at maximizing performance, would be capable of analyzing such physiological and behavior markers online to further change the level of automation when it is relevant for the mission purpose.