This paper studies the joint optimal resource allocation and probabilistic caching design for device-to-device (D2D) communications in a wireless heterogeneous network with full-duplex (FD) relays. In particular, popular contents can be cached at user devices as well as at relays that are located close to users. A user can request contents from another user via D2D communications and also from a nearby relay equipped with FD radios. In the case that there is a caching miss (i.e., the requested contents are not found at the other users/relays within the coverage range), users can connect to the base station via a relay by using the FD communication technology. Subsequently, we develop mathematical models to analyze the throughput performance with edge caching where both cochannel system level interference and FD self-interference are considered. Due to the high complexity of stochastic optimization, we develop low-complexity optimization formulation by decomposing the original problem into three simple subproblems that can be efficiently solved. Finally, numerical results are presented to illustrate developed theoretical findings in the paper and significant performance gains of the throughput performance.