Conversational interactions extend beyond verbal exchange, involving dynamic synchronisation across physiological, emotional, and acoustic domains. This study aimed to characterise multimodal speaker-listener coupling during structured debates to examine how bidirectional dynamics relate to autonomic regulation, signal complexity, and emotional states. We analysed data from the K-EmoCon database, which included 32 participants in 10-minute debates. Heart rate variability (HRV) features, speech features, and multi-perspective emotion annotations were synchronised and analysed in segmented speak-listen phases. Cross-correlation and bidirectional coupling quantified coupling strength and directionality, and their relationships with emotional states were assessed. Negative lag segments showed significantly higher HRV features, including AVNN (0.655 [0.631-0.749], p = 0.003), HF power (0.620 [0.338-0.781], p < 0.001), and SD1 (1.30x10-3 [1.19-1.41]x10-3, p = 0.003). Positive lag segments were associated with higher sample entropy (0.058 [0.046-0.065], p < 0.001) and diffusion entropy (μr: 1.209 [1.201-1.221], p < 0.001). Lower emotion states (1-2) tended to exhibit negative-lag dynamics, whereas moderate to high states (3 and 5) showed a modest positive-lag predominance. Multimodal coupling reveals distinct physiological and emotional signatures linked to leadership and responsiveness in conversation, providing insights for therapeutic, educational, and collaborative applications.