In 5G and beyond network architectures, operators and content providers base their content distribution strategies on Heterogeneous Networks, where macro and small cells are combined to offer better Quality of Service to wireless users. On top of such networks, edge caching and Coordinated Multi-Point (CoMP) joint transmissions are used to further improve performance. In this paper, we address the average delay minimization problem by first formulating it as a static optimization problem. Even though the problem is NP-hard we are able to solve it via an efficient algorithm that guarantees a 1 2-approximation ratio. We then proceed to propose two fully distributed and dynamic caching policies for the same problem. The first one asymptotically converges to the static optimal solution under the Independent Reference Model (IRM). The second one provides better results in practice under real (nonstationary) request processes. Our online policies outperform existing dynamic solutions that are PHY-unaware.