In recent years, the capacity of cellular networks has hardly kept pace with the dramatic explosion of cellular traffic from emerging mobile applications. To address this issue, a number of studies have been proposed to offload the cellular traffic using delay-tolerant networks (DTNs) opportunistically formed by mobile devices. These offloading schemes rely on the assumption of small-size content, which can be entirely transmitted over a single DTN contact. However, such an assumption, which was probably valid in the past, can no longer hold with the increasing popularity of large-size multimedia contents in the future. In this paper, we propose a novel contact-duration-aware offloading scheme called Coff, which consists of several designs that are specially tailored for DTNs. First, we use content fragmentation to utilize short contacts. Second, we adopt network coding to achieve a near-optimum dissemination. Finally, we design a greedy load allocation (GLA) algorithm to achieve no less than $(\mbox{1}-\mbox{1}/e)$ of the optimum. Extensive simulations on both synthetic and real-world traces show that Coff is more efficient than the baselines, which extend from state-of-art DTN-based offloading schemes with content fragmentation and network coding.