Macrocells are expected to be densely overlaid by small cells (SCs) to meet the increasing capacity demands. Due to their dense deployment, some SCs will not be connected directly to the core network and thus they may forward their traffic to the neighboring SCs until they reach it, thereby forming a multi-hop backhaul (BH) network. This is a promising solution, since the expected short length of BH links enables the use of millimeter wave (mmWave) frequencies to provide high capacity BH. In this context, user association becomes challenging due to the multihop BH architecture and therefore new optimal solutions should be developed. Thus, in this paper, we study the user association problem aiming at the joint maximization of network energy and spectrum efficiency, without compromising the user quality of service. The problem is formulated as an "-constraint problem, which considers the transmit energy consumption both in the access network, i.e., the links between the users and their serving cells, and the BH links. The optimal Pareto front solutions of the problem are analytically derived for different BH technologies and insights are gained into the energy and spectrum efficiency trade-off. The proposed optimal solutions, despite their high complexity, can be used as a benchmark for the performance evaluation of user association algorithms. We also propose a heuristic algorithm, which is compared with reference solutions under different traffic distribution scenarios and BH technologies. Our results motivate the use of mmWave BH, while the proposed algorithm is shown to achieve near-optimal performance.