This paper investigates the resource allocation problem in non-orthogonal multiple-access (NOMA) cellular networks underlaid with OMA-based device-to-device (D2D) communication. This network architecture enjoys the intrinsic features of NOMA and D2D communications; namely, spectral efficiency, massive connectivity, and low-latency. Despite these indispensable features, the combination of NOMA and D2D communications exacerbates the resource allocation problem in cellular networks due to the tight coupling among their constraints and conflict over access to shared resources. The aim of our work is to maximize the downlink network sum-rate, while meeting the minimum rate requirements of the cellular tier and underlay D2D communication, and incorporating interference management as well as other practical constraints. To this end, many-to-many matching and difference-of-convex programming are employed to develop a holistic sub-channels and power allocation algorithmic solution. In addition to analyzing the properties of the proposed solution, its performance is benchmarked against an existing solution and the traditional OMA-based algorithm. The proposed solution demonstrates superiority in terms of network sum-rate, users