Halliday & Matthiessen (2014: 661, 663):
Interpersonal. Propositions/proposals combine to form patterns of exchange involving two or more interactants… . At least in some registers such as interviews, classroom discourse and quiz shows, the patterns are regular and predictable enough to appear to be compositional in nature: interpersonal units of exchange consisting of certain sequences of propositions/proposals. But whatever the status is of such exchange patterning, the critical point is that it is interpersonal rather than textual or ideational, and that it is intermediate between propositions/proposals and the whole text.