In this paper, we propose a novel joint resource allocation and cooperative caching scheme for power-domain non-orthogonal multiple access (PD-NOMA)-based heterogeneous networks (HetNets). In our scheme, the requested content is fetched directly from the edge if it is cached in the storage of one of the base stations (BSs), and otherwise is fetched via the backhaul. Our scheme consists of two phases: 1) Caching phase where the contents are saved in the storage of the BSs; and 2) Delivery phase where the requested contents are delivered to users. We formulate a novel optimization problem over radio resources and content placement variables. We aim to minimize the network cost subject to quality-of-service (QoS), caching, subcarrier assignment, and power allocation constraints. By exploiting advanced optimization methods, such as alternative search method (ASM), Hungarian algorithm, successive convex approximation (SCA), we obtain an efficient sub-optimal solution of the optimization problem. Numerical results illustrate that our ergodic caching policy via the proposed resource management algorithm can achieve a considerable reduction on the total cost on average compared to the most popular caching and random caching policy. Moreover, our cooperative NOMA scheme outperforms orthogonal multiple access (OMA) in terms of the delivery cost in general with an acceptable complexity increase.