In the area of full duplex (FD)-enabled small cell networks, limited works have been done on consideration of cache and mobile edge communication (MEC). In this paper, a virtual FD-enabled small cell network with cache and MEC is investigated for two heterogeneous services, high-data-rate service and computation-sensitive service. In our proposed scheme, content caching and FD communication are closely combined to offer high-data-rate services without the cost of backhaul resource. Computing offloading is conducted to guarantee the delay requirement of users. Then we formulate a virtual resource allocation problem, in which user association, power control, caching and computing offloading policies and resource allocation are jointly considered. Since the original problem is a mixed combinatorial problem, necessary variables relaxation and reformulation are conducted to transfer the original problem to a convex problem. Furthermore, alternating direction method of multipliers (ADMM) algorithm is adopted to obtain the optimal solution. Finally, extensive simulations are conducted with different system configurations to verify the effectiveness of the proposed scheme.