In this paper, a novel dual-mode scheduling framework is proposed that jointly performs user applications (UA) selection and scheduling over microwave ($μ$W) and millimeter wave (mmW) bands. The proposed scheduling framework utilizes a set of context information, including the channel state information, the delay tolerance and required load per UA, and the uncertainty of mmW channels, to maximize the quality-of-service (QoS) per UA. The scheduling problem is formulated as an optimization with minimum unsatisfied relations (min-UR) problem which is shown to be challenging to solve. Consequently, a long-term scheduling framework, consisting of two stages, is proposed. Within this framework, first, the scheduling over $μ$W band is formulated as a matching game and to solve this problem, a novel algorithm is proposed and shown to yield a two-sided stable resource allocation. Second, over the mmW band, the scheduling problem is formulated as a 0-1 Knapsack problem and a novel algorithm is proposed to solve it. Furthermore, it is shown that the proposed framework can find an effective scheduling solution, over both $μ$W and mmW, in polynomial time. Simulation results show that, compared with conventional scheduling schemes, the proposed approach significantly increases the number of satisfied UAs and enhances the users' quality-of-experience.