Abstract <p>This paper aims to construct the Darboux transformation as well as derive two types of solutions for the complex coupled dispersionless (CCD) equation on time scales. The Lax pair is directly constructed to obtain the CCD equation on time scales, which unifies the semi-discrete, fully discrete, continuous and <i>q</i>-deformed CCD equations. Thereafter, the <i>N</i>-fold Darboux transformation of this equation is proposed on time scales. In the case of zero seed solution, one-soliton and multi-soliton solutions on time scales are obtained. One-breather and multi-breather solutions are constructed from a nonzero seed solution. Moreover, the dynamics of soliton and breather solutions are discussed on various time scales. This work provides a novel approach to unify the CCD equation, which is essential to investigate the dynamic behaviors of its solutions across both continuous and discrete hierarchies.</p> Graphic Abstract <p></p>