In recent years, integration and heterogeneous of network have become the two major characteristics of the future evolution about wireless communication. In this paper, multi-hop WIFI/LTE networks and dual-mode single communication mobile terminals, i.e. integral association, are considered in flat converged network. With the constraint of Quality of Service (QoS) for emergency service and load balance, a distributed optimization algorithms is constructed by jointing power control, vertical handoff and routing. More specifically, the framework model of network is represented by a generalized network utility maximization (NUM) problem. Furthermore, achieving utility maximization is proved to be NP-hard. Then, a generic framework is given to simplify the problem to arrive a distributed optimization algorithm. Simulation results show that the distributed algorithm can approach the optimal solution. Compared with greedy algorithm, the proposed one is able to improve the network utility on the basis of ensuring load balancing as much as possible.