Cellular network operators are striving to solve the problem caused by the increasing volume of traffic over their networks. Given the proliferation of multi-interface devices, offloading part of the traffic to available access networks (e.g., WiFi or 3G access networks, even from other operators) seems to be a promising alternative. Here, we propose an IMS-compatible solution for flow mobility between access networks that exhibits two key features: flow mobility is transparent to both local applications at mobile nodes and their communication peers (e.g., multimedia content servers), and mobility operations are assisted by the network, so the home network supports the terminal in the process of access network discovery, and provides the terminal with policies that meet visited and home operators' roaming agreements while optimizing the use of their networks. The proposed solution has been validated using a real IMS testbed with Ethernet and WiFi access networks, where the mobility of UDP and TCP flows has been tested.