This paper examines how the structural features of engineering engagement programs (EEPs) are related to the nature of their service-learning partnerships. "Structure" refers to formal and informal models, processes, and operations adopted or used to describe engagement programs, while "nature" signifies the quality of interactions or interpersonal dynamics within partnerships. We developed the Transactional, Cooperative, and Communal (TCC) framework to code interviews (N=30) with community partners, administrators, faculty members, and students at three well-developed and geographically-diverse EEPs. A thematic analysis approach was then employed to relate the three TCC partnership natures to six emergent structural themes: (a) program purposes, (b) partnership structures, (c) modes of interactions, (d) organizational partners, (e) individual partners and advisors, and (f) projects. The paper concludes by discussing specific implications of the TCC framework for educators and program administrators, the importance of recognizing both individual and organizational influences on partnerships, and the salience of engineering education as a context for service-learning and community engagement (SLCE) programs.