Recent research has extensively reported the phenomenon of inter-brain neural coupling between speaker and listener during speech communication. Yet, the specific speech processes underlying this neural coupling remain elusive. To bridge this gap, this study estimated the correlation between the temporal dynamics of speaker-listener neural coupling with speech features, utilizing two inter-brain datasets accounting for different noise levels and listener's language experiences (native vs. non-native). We first derived time-varying speaker-listener neural coupling, extracted acoustic feature (envelope) and semantic features (entropy and surprisal) from speech, and then explored their correlational relationship. Our findings reveal that in clear conditions, speaker-listener neural coupling correlates with semantic features. However, as noise increases, this correlation is only significant for native listeners. For non-native listeners, neural coupling correlates predominantly with acoustic feature rather than semantic features. These results revealed how speaker-listener neural coupling associated with the acoustic and semantic features under various scenarios, enriching our understanding of the inter-brain neural mechanisms during natural speech communication. We therefore advocate for more attention on the dynamic nature of speaker-listener neural coupling and its modelling with multi-level speech features.