Offloading is a promising technique for alleviating the ever-growing traffic load from infrastructure-based networks such as the Internet. Offloading consists in using alternative methods of transmission as a cost-effective solution for network operators to extend their transport capacity. In this paper, we advocate the use of conventional vehicles equipped with storage devices as data carriers whilst being driven for daily routine journeys. The road network can be turned into a large-capacity transmission system to offload bulk transfers of delay-tolerant data from the Internet. The challenges we address include how to assign data to flows of vehicles and while coping with the complexity of the road network. We propose an embedding algorithm that computes an offloading overlay where each logical link spans over multiple stretches of road from the underlying road infrastructure. We then formulate the data transfer assignment problem as a novel linear programming model we solve to determine the optimal logical paths matching the performance requirements of a data transfer. We evaluate our road traffic allocation scheme using actual road traffic counts in France. The numerical results show that 20% of vehicles in circulation in France equipped with only one Terabyte of storage can offload Petabyte transfers in a week.