Steel–concrete composite reinforcement technology has developed rapidly in recent years. This method has emerged as one of the best reinforcement alternatives in bustling sections because it saves time and space. In this paper, a combination reinforcement plan for single-column piers in curved bridges is proposed, with its interface performance being comprehensively investigated. Nine sets of comparative experiments were conducted to analyze the key issue of shear resistance at the interface between new and old concrete in the combination reinforcement scheme. It was found that under the proposed circumferential reinforcement structure, the stress changed from interface shear to overall compression; therefore, both ductility and the failure bearing capacity were improved owing to the Poisson effect in the later stage of the interface treatment component. Meanwhile, using the calculation formulas in existing reinforcement specifications, we introduce the shear strength parameters under a new "serrated groove" situation, which has higher bearing capacity than the commonly used chiseling and groove modes. The methodology and findings of this study supplement the single-column pier combination reinforcement for existing bridges in urban sections and lays the foundation for future research.