To map the associations between affective, cognitive, and behavioral components of engagement with digital health interventions to provide a framework to improve intervention design, evaluation, and impact. An exploratory multiple case study examined 3 studies evaluating a childhood obesity mobile application (NoObesity, data collection: from September 15, 2020 to June 23, 2021), a mental health conversational agent mobile application (Wysa, data collection: from December 13, 2022 to July 31, 2023), and a telephone-delivered conversational agent postsurgical assessment (Dora R1, data collection: from September 17, 2021 to January 31, 2022). Qualitative data from semi-structured interviews (NoObesity: n=15, Wysa: n=4, and Dora R1: n=20) was analyzed using a codebook thematic analysis approach to generate models mapping engagement. A cross-case analysis compared the 3 models with a hypothesized model. The case studies highlighted close associations between affective, cognitive, and behavioral components throughout the engagement process. Similar patterns of engagement were generated from the case studies, but these patterns differed from the literature-based hypothesized model in the order of influence of cognitive and affective engagement. Understanding how different components of engagement interact is essential for designing interventions that mitigate barriers to engagement and maximize intervention impact. The framework provides a preliminary guide and recommendations for how to support particular components. Future research on the order of cognitive and affective components (or importance thereof) and testing the influence of particular features on engagement components could improve the framework and clinical impact. clinicaltrials.gov Identifier: NoObesity: NCT05261555; Wysa: NCT05533190; Dora R1: NCT05213390.