The study explores interbrain neural coupling when interlocutors engage in a conversation whether it be in their native or nonnative language. To this end, electroencephalographic hyperscanning was used to study brain-to-brain phase synchronization during a two-person turn-taking verbal exchange with no visual contact, in either a native or a foreign language context. Results show that the coupling strength between brain signals is increased in both, the native language context and the foreign language context, specifically, in the alpha frequency band. A difference in brain-to speech entrainment to native and foreign languages is also shown. These results indicate that between brain similarities in the timing of neural activations and their spatial distributions change depending on the language code used. We argue that factors like linguistic alignment, joint attention and brain-entrainment to speech operate with a language-idiosyncratic neural configuration, modulating the alignment of neural activity between speakers and listeners. Other possible factors leading to the differential interbrain synchronization patterns as well as the potential features of brain-to-brain entrainment as a mechanism are briefly discussed. We concluded that linguistic context should be considered when addressing interpersonal communication. The findings here open doors to quantifying linguistic interactions.