The optimization of the base station (BS) assignment problem in mobile access networks is a primary task towards enabling efficient utilization of network resources. So far, this problem has been mainly studied in terms of air interface optimization. In this paper, we present a novel BS assignment strategy that integrates backhaul constraints in the user assignment criterion. The motivation of this strategy is the fact that in some scenarios the backhaul can become the network bottleneck. The BS assignment problem or user allocation problem is formulated using a utility-based framework. We take into consideration key aspects such as the revenue associated to each type of service along with the resource consumption in terms of both radio and backhaul resources. Results are given in a multi-service scenario for guaranteed rate services.