In this paper, device-to-device (D2D)-assisted caching is considered to offload traffic from the capacity-stringent backhaul networks to the proximity of users. First, a three-layer hierarchical content provision model is established, where a requested content can be fetched from the local cache directly, from the cache of a proximal device through D2D communications, or from the serving base station through backhaul transmissions. Then, for a general multi-unit-cache equipped at each device, we propose independent content placement in each cache unit and correlated content placement in each cache unit without repetition, based on which the problem of maximizing the edge cache hit ratio is formulated. Instead of optimizing the caching probability for all contents in the library, we propose a parameter-based caching framework based on a truncated Zipf distribution, where only the position of truncation and the Zipf exponent are involved. For jointly determining the optimal values of the two parameters, a genetic algorithm and a two-step search algorithm are designed. The simulation results demonstrate that the correlated content placement outperforms its independent counterpart, and significant performance gains can be achieved by the proposed parameter-based caching framework in comparison with most existing approaches.