In conversation, individuals work together to achieve communicative goals, complementing and aligning language and body with each other. An important emerging question is whether interlocutors entrain with one another equally across linguistic levels (e.g., lexical, syntactic, and semantic) and modalities (i.e., speech and gesture), or whether there are complementary patterns of behaviors, with some levels or modalities diverging and others converging in coordinated fashions. This study assesses how kinematic and linguistic entrainment interact with one another across levels of measurement, and according to communicative context. We analyzed data from two matched corpora of dyadic interaction between—respectively—Danish and Norwegian native speakers engaged in affiliative conversations and task-oriented conversations. We assessed linguistic entrainment at the lexical, syntactic, and semantic level, and kinetic alignment of the head and hands using video-based motion tracking and dynamic time warping. We tested whether—across the two languages—linguistic alignment correlates with kinetic alignment, and whether these kinetic-linguistic associations are modulated either by the type of conversation or by the language spoken. We found that kinetic entrainment was positively associated with low-level linguistic (i.e., lexical) entrainment, while negatively associated with high-level linguistic (i.e., semantic) entrainment, in a cross-linguistically robust way. Our findings suggest that conversation makes use of a dynamic coordination of similarity and complementarity both between individuals as well as between different communicative modalities, and provides evidence for a multimodal, interpersonal synergy account of interaction.