A storage module includes a dynamic random access memory (DRAM) device, a nonvolatile memory device, and a high-speed buffer memory. An method of operating the storage module includes copying target data stored in the nonvolatile memory device to the high-speed buffer memory in response to an external device entering a page fault mode, receiving a first refresh command from the external device, and, in response to the first refresh command, performing a first refresh operation associated with the DRAM device and moving the target data copied to the high-speed buffer memory to the DRAM device during a first refresh reference time.