The heterogeneous fog radio access networks (Fog-RAN), the integration of fog computing, and traditional heterogeneous radio access networks can be implemented through the next-generation wireless communication networks. However, most of the solutions are limited to the spectrum efficiency optimization, and cross-tier interference existing in the fog access points (F-APs) could affect the network performance seriously. In this paper, the user association, resource allocation (including bandwidth and power), and caching deployment are investigated in the heterogeneous Fog-RAN to consider energy efficiency and cross-tier interference mitigation. Specifically, the user association, resource allocation, and caching strategy are formulated as a non-convex optimization problem and then transformed into a convex problem, which can be solved by a proposed algorithm based on the concept of the alternating direction method of multipliers (ADMM). Then an ADMM-based algorithm is proposed to enhance the energy efficiency of the Fog-RAN. Compared with the current solutions, simulation results illustrate the proposed algorithm’s convergence and effectiveness.