This paper considers a dual-channel supply chain consisting of a manufacturer and a capital-constrained retailer, where the retailer makes certain sales efforts and the manufacturer may hitch a ride on the retailer’s sales efforts. Deferred payment and bank loan financing models under Retailer- and Manufacturer-Stackelberg settings are established, respectively. The equilibrium price and sales effort strategies of both sides of the supply chain under two power structures and financing modes are obtained by the backward solution method, and then the influence of free-riding behavior and financing interest rate on equilibrium strategies is explored, as well as how the power structure affects the financing decisions of enterprises. The results show that deferred payment is more conducive to retailers’ sales effort and order volume, which is the optimal financing model for the retailers under each power structure. Power structure affects the initial capital threshold of retailers and the manufacturers’ financing decisions. The impact of free-riding behavior and financing rate on equilibrium prices exists and varies, depending on the power structure and financing model. Numerical simulation results show that manufacturers should give priority to publishing price strategies, while retailers should decide whether to give priority to publishing price strategies according to financing mode and cross-price sensitivity. This paper’s findings can provide valuable guidance for decision-making in financing, price, and sales effort for the capital-constrained dual-channel supply chain.