D2D offloading reduces the load of cellular network by asking mobile nodes to download content directly from storage of neighboring helpers via short range links. In this paper, we introduce a novel storage assignment scheme that can enhance storage utilization for D2D networks that have different types of storage nodes. Unlike traditional D2D systems that only use storage as static content cache, our scheme uses on-demand relaying to enhance storage utilization. Our on-demand relaying scheme replicates rare content when it is requested. Therefore, the proposed scheme can greatly increase the amount of content supported by the offloading system. We develop a convex optimization based algorithm to find the optimal storage assignment tradeoff between static caching and on-demand relaying. Numerical results and real-world trace-driven simulations show that our algorithm can achieve 30% reduction in offloading failure rate compared to static schemes.