The Heterogeneity Inclusion and Mobility Adaptation through Locator ID Separation (HIMALIS) architecture natively supports mobility and multihoming by allowing the host to change its address (or locator) used in the network layer while keeping the session identifier used in the application and transport layers unchanged. It also facilitates faster updates of ID/locator mappings in name resolution servers or registries. However, it still lacks functions for supporting seamless host mobility when a host moves across edge networks and network mobility when a whole edge network moves. To address these issues, this paper presents an optimized host mobility management scheme and a network mobility management scheme. These schemes employ traffic redirection from the old gateway (or old access router) to the new gateway (or new access router) to reduce packet loss during handovers. Meanwhile, the intrinsic security functions of the HIMALIS architecture are leveraged to protect the newly introduced mobility schemes from various attacks such as impersonation and man-in-the-middle attacks.