Digital health assistants (DHAs) are conversational agents incorporated into health systems’ interfaces, exploiting an intuitive interaction format appreciated by the users. At the same time, however, their conversational format can evoke interactional practices typical of health encounters with human doctors that might misguide the users. Awareness of the similarities and differences between novel mediated encounters and more familiar ones helps designers avoid unintended expectations and leverage suitable ones. Focusing on adherence apps, we analytically discuss the structure of DHA-patient encounters against the literature on physician-patient encounters and the specific affordances of DHAs. We synthesize our discussion into a design checklist and add some considerations about DHA with unconstrained natural language interfaces.