Monitoring cognitive workload has the potential to improve both the performance and fidelity of human decision making. However, previous efforts towards discriminating further than binary levels (e.g., low/high or neutral/high) in cognitive workload classification have not been successful. This lack of sensitivity in cognitive workload measurements might be due to individual differences as well as inadequate methodology used to analyse the measured signal. In this paper, a method that combines the speech signal with cardiovascular measurements for screen and heartbeat classification is introduced. For validation, speech and cardiovascular signals from 97 university participants and 20 airline pilot participants were collected while cognitive stimuli of varying difficulty level were induced with the Stroop colour/word test. For the trinary classification scheme (low, medium, high cognitive workload) the prominent result using classifiers trained on each participant achieved 15.17 ± 0.79% and 17.38 ± 1.85% average misclassification rates indicating good discrimination at three levels of cognitive workload. Combining cardiovascular and speech measures synchronized to each heartbeat and consolidated with short-term dynamic measures might therefore provide enhanced sensitivity in cognitive workload monitoring. The results show that the influence of individual differences is a limiting factor for a generic classification and highlights the need for research to focus on methods that incorporate individual differences to achieve even better results. This method can potentially be used to measure and monitor workload in real time in operational environments.