The mapping of information structure onto morphology or intonation varies greatly crosslinguistically. Agglutinative languages, like Inuktitut or Quechua, have a rich morphological layer onto which discourse-level features are mapped but a limited use of intonation. Instead, English or Spanish lack grammaticalized morphemes that convey discourse-level information but use intonation to a relatively large extent. We propose that the difference found in these two pairs of languages follows from a division of labor across language modules, such that two extreme values of the continuum of possible interactions across modules are available as well as combinations of morphological and intonational markers. At one extreme, in languages such as Inuktitut and Quechua, a rich set of morphemes with scope over constituents convey sentence-level and discourse-level distinctions, making the alignment of intonational patterns and information structure apparently redundant. At the other extreme, as in English and to some extent Spanish, a series of consistent alignments of PF and syntactic structure are required to distinguish sentence types and to determine the information value of a constituent. This results in a complementary distribution of morphology and intonation in these languages. In contact situations, overlap between patterns of module interaction are attested. Evidence from Quechua–Spanish and Inuktitut–English bilinguals supports a bidirectionality of crosslinguistic influence; intonational patterns emerge in non-intonational languages to distinguish sentence types, whereas morphemes or discourse particles emerge in intonational languages to mark discourse-level features.