Content delivery network (CDN) interconnection is a promising solution to addressing the limited service scale of CDNs. It scales the CDN's service footprint through the cooperation of CDNs without significantly changing the existing network architecture. However, in a CDN interconnection system, CDNs are independent of each other and each pursues its own goals, which means that cooperation is hard to establish and easy to break. In our paper, we propose a stable marriage-based routing framework to establish a strong cooperation service for CDNs and to select the `optimal' server for each request among the cooperative CDNs. To this end, we first investigate the relationship between the service cost and the service profit of CDN interconnection, and we design a price determination strategy to ensure the economic interests of each cooperative CDN, which is helpful in establishing a stable CDN cooperation service. Then we propose a dynamic request routing strategy to select the `optimal' server for each end user request by applying the `stable match' theory. This strategy is helpful in scaling the CDN service footprints with guaranteed service quality and in gaining more profit with lower service costs. The simulation results show that our frameworks can scale the CDN's service footprints with guaranteed service quality and gain more services without increasing service costs. Furthermore, our frameworks are win-win request routing frameworks because they help the upstream CDN of the CDN interconnection to increase service profit without increasing its cost. Moreover, they help the downstream CDNs of the CDN interconnection to gain extra revenue by using their idle resources.