Collaborative green transformation across industrial chains has become an important driver for the achievement of the dual-carbon goals. Existing research has mainly focused on the horizontal diffusion of green innovation within industries. Insufficient attention has been paid to the vertical transmission mechanism of green innovation along supply chains. The different roles of constraint and spillover mechanisms in this process have also not been fully distinguished. From the perspective of vertical trading relationships, Chinese A-share listed firms from 2013 to 2024 were selected as the sample. The transmission effects of green innovation in supply chains and their boundary conditions were empirically examined. It is found that an increase in the green innovation level of focal firms significantly promotes green innovation among upstream suppliers. No significant effect is found on green innovation among downstream customers. Further analysis shows that the backward transmission effect is significantly strengthened by stronger vertical market power of focal firms. Mechanism analysis indicates that upstream suppliers' green innovation is mainly promoted through increased green investment by suppliers. Heterogeneity analysis shows that both substantive green innovation and strategic green innovation among suppliers are significantly promoted by focal firms' green innovation. The backward transmission effect is also found to be more pronounced when suppliers have higher levels of digitalization, stronger dependence on focal firms, and shorter geographic distance from focal firms, and when focal firms exhibit better ESG performance. The internal logic of the vertical transmission of green innovation along supply chains is thus revealed. Empirical evidence is also provided for the coordinated green transformation of industrial chains.