In heterogeneous networks (HetNets), different lower-power base stations are added in a typically unplanned manner to the well-planned macro-only network, bringing new challenges to the network functions. Small cells experience limited backhaul capacity since cost-effective backhaul is not easily accessible to them. This study focuses on the issue of user association in backhaul-constrained HetNets. It shows that it is necessary to associate users with cells using a load balancing approach in order to fully leverage the addition of small cells. The cell association needs to be done jointly with an interference management technique that protects offloaded users and those prone to harmful interference. After modeling the system and describing the interference model, the problem of cell and subband allocation is formulated. We first examine the problem in a time-sharing mode and present a centralized heuristic solution to the cell and subband allocation problem. This is accomplished by solving the convex problem using the gradual removal method. The importance of providing distributed algorithms for HetNets leads to the development of a new algorithm through the application of the dual decomposition method to a reformulated problem and the use of an admission control mechanism. In the achieved algorithm, all computations are performed locally, with each user and base station relying only on local information. This algorithm obtains near-optimal answers, as confirmed by the simulation results. Compared with conventional cell allocation methods, our distributed algorithm prevents intensive interference for all users and achieves better load balance between network tiers, resulting in improved network utility.