Coalescing RDMA and Persistent Memory (PM) delivers high end-to-end performance for networked storage systems, which requires rethinking the design of efficient hash structures. In general, existing hashing schemes separately optimize RDMA and PM, thus partially addressing the problems of RDMA Access Amplification and High-Overhead PM Consistency. In order to address these problems, we propose a continuity hashing, which is a one-stone-two-birds design to optimize both RDMA and PM. The continuity hashing leverages a fine-grained contiguous shared region, called SBuckets, to provide standby positions for the neighbouring two buckets in case of hash collisions. In the continuity hashing, remote read only needs a single RDMA read to directly fetch the home bucket and the neighbouring SBuckets, which contain all the positions of maintaining a key-value item, thus alleviating RDMA access amplification. Continuity hashing further leverages indicators that can be atomically modified to support log-free PM consistency for all the write operations. Evaluation results demonstrate that compared with state-of-the-art schemes, continuity hashing achieves high throughput (i.e., 1.45X -- 2.43X improvement), low latency (about 1.7X speedup) and the smallest number of PM writes with various workloads, while has acceptable load factors of about 70%.