Structured overlay networks are widely used as platforms for distributed systems. However, in a high churn situation, it is highly costly to maintain the structure and service availability of an overlay network because there is a limitation in churn handling. Several cooperation mechanisms among overlay networks are proposed to improve service availability of overlay networks in a high-churn situation. Several cooperation mechanisms are proposed among overlay networks. The cooperation mechanisms can group structured overlay networks to simplify routing functions. However, the existing mechanisms do not consider managing churn information among overlay networks. In this paper, we propose a new framework that can share states of the nodes and spread churn information to neighbor nodes among different overlay networks. Using our framework, we are able to maintain each overlay network effectively and improve the reachability of messages under churn. We evaluate our framework with Chord, Kademlia, and Pastry. Our framework improves the detection time of churn by about 30% and decreases the stabilization messages by about 30-40%. We discuss combinatorial effects of the sharing state of the nodes among different overlay networks.