In the context of a dual-channel supply chain comprising a solitary retailer and a single manufacturer, we explore the ramifications of the manufacturer’s discount offered to the retailer and the bank loan interest rate on optimal pricing decisions and carbon emission reduction efforts within the dual-channel supply chain. This exploration is conducted under the framework of a financing strategy that combines bank loans with advance payments, considering the financial limitations of both the manufacturer and the retailer. By utilizing the Stackelberg game model and conducting numerical simulations, we uncover that an augmentation in the discount rate provided by the manufacturer to the retailer diminishes the manufacturer’s profits and carbon abatement funds, while augmenting the retailer’s overall profit. Furthermore, a decline in the bank lending rate leads to a reduction in the retailer’s wholesale cost, motivating the retailer to adopt a more aggressive pricing approach and lower both online and offline selling prices to stimulate demand and bolster market competitiveness. Conversely, excessively high lending rates prompt retailers to elevate their selling prices, resulting in decreased sales volumes and potentially adverse effects on overall profits. Hence, an intricate and dynamic relationship exists between retailers’ financing expenses, their sales strategies, and profit margins. Consequently, retailers must meticulously evaluate market dynamics to devise effective pricing strategies, which generally yield higher profits compared to uniform pricing approaches.