To cope with the explosive traffic demands and limited capacity provided by the current cellular networks, Delay Tolerant Networking (DTN) is used to migrate traffic from the cellular networks to the free and high capacity device-todevice networks. The current DTN-based mobile data offloading models do not address the heterogeneity of mobile traffic and are based on simple network assumptions. In this paper, we establish a mathematical framework to study the problem of multiple mobile data offloading under realistic network assumptions, where 1) mobile data is heterogeneous in terms of size and lifetime, 2) mobile users have different data subscribing interests, and 3) the storage of offloading helpers is limited. We formulate the maximum mobile data offloading as a Submodular Function Maximization problem with multiple linear constraints of limited storage and propose greedy, approximated and optimal algorithms for different offloading scenarios. We show that our algorithms can effectively offload data to DTNs by extensive simulations which employ real traces of both humans and vehicles.