Stress in interpreting has been well researched over the last few decades. This study takes a multimodal approach to investigate the distinct effects of emotional and cognitive load on interpreter stress. 20 student interpreters consecutively interpreted four first-person mental healthcare narratives from Turkish to English that varied in emotional content and difficulty, within a 2×2 factorial design. Cognitive and emotional responses were captured using galvanic skin response (GSR), prosodic features (pitch and intensity), and three self-report measures (PANAS, STAI, and NASA-TLX). The stimuli were normed using traditional readability indices, expert ratings, and novel natural language processing techniques to control emotional valence and linguistic complexity. The results showed that physiological arousal, as measured by GSR, was primarily driven by cognitive load, particularly during the later stages of interpreting. Emotional load, on the other hand, was more clearly reflected in prosodic markers (especially pitch) and negative affect ratings. The results also hinted at a convergence in pitch between the source speaker and the interpreter. Notably, emotional and cognitive load began to take its toll from the latter stages of the listening phase onwards. However, none of the objective or subjective stress measures predicted interpreting accuracy, suggesting that performance may be mediated by individual coping strategies. The findings are expected to have implications for interpreting pedagogy and the development of cognitive and emotional support strategies in high-stakes interpreting contexts.