Hybrid arrays enable millimeter-wave (mmW) base stations and users to steer multiple beams simultaneously. However, in dense mmW networks with small inter-site distances and many users, a large number of serving beams can lead to significant inter- and intra-cell interference that prevents data-hungry users from satisfying their rate requirements. In this work, we address this problem by designing a linear multi-step optimization framework for user association and beam scheduling with interference management. In the first step, the framework aims to maximize the number of users with fully satisfied rate requirements by scheduling a minimal number of non-interfering beams. In the second step, any remaining non-interfering beams are distributed among other users to maximize the number of them with at least partially satisfied requirements. Hybrid precoders and combiners are then designed to remove any excess sidelobe interference among the scheduled beams. Finally, power allocation is optimized on a network level to boost the data rates of the partially satisfied users. Given that the framework includes NP-hard optimization problems, we propose an algorithm that attains a sub-optimal solution in polynomial-time. The proposed framework is numerically evaluated in realistic mmW channels and the results reveal its advantages over the baseline user association schemes.