Assessing drivers’ mental workload is crucial for reducing road accidents. This study examined drivers’ mental workload in a simulated auditory-based dual-task driving scenario, with driving tasks as the main task, and auditory-based N-back tasks as the secondary task. A total of three levels of mental workload (i.e., low, medium, high) were manipulated by varying the difficulty levels of the secondary task (i.e., no presence of secondary task, 1-back, 2-back). Multimodal measures, including a set of subjective measures, physiological measures, and behavioral performance measures, were collected during the experiment. The results showed that an increase in task difficulty led to increased subjective ratings of mental workload and a decrease in task performance for the secondary N-back tasks. Significant differences were observed across the different levels of mental workload in multimodal physiological measures, such as delta waves in EEG signals, fixation distance in eye movement signals, time- and frequency-domain measures in ECG signals, and skin conductance in EDA signals. In addition, four driving performance measures related to vehicle velocity and the deviation of pedal input and vehicle position also showed sensitivity to the changes in drivers’ mental workload. The findings from this study can contribute to a comprehensive understanding of effective measures for mental workload assessment in driving scenarios and to the development of smart driving systems for the accurate recognition of drivers’ mental states.