As wireless Internet applications are proliferating and becoming the main driver for the exploding growth of wireless access technologies, integrating third generation (3G) systems with Wi-Fi networks allows combining the strengths of these two technologies. In this paper, we present a novel design for a dual-mode user equipment (UE) model that supports both 3G and Wi-Fi access and provide one implementation using the OPNET simulation tool. The proposed UE model should be capable of supporting all the integrated network architectures depending on the deployment scenario. The modular model is equipped with two air-interface modules that allow communication with 3G and Wi-Fi networks, but the rest of the protocol stack is the standard IP protocol stack to satisfy the compatibility requirement. The design also includes needed functionalities to support vertical handoff across the two networks. The paper also presents an example algorithm that may be implemented into the proposed UE for enhanced gateway selection.