In the vehicle routing literature it is generally assumed that each vehicle is driven by a single driver from the beginning to the end of its route. We introduce a new vehicle routing problem without this assumption. We consider a problem with two depots in which vehicles must departure from one depot and arrive to the other, while drivers should leave and return to the same depot and their routes can not exceed a given duration. Under these conditions, changes of vehicle are mandatory for the drivers in order to go back to their base depots. These changes can only take place at some particular nodes. Moreover, vehicles and drivers must be synchronized. We model the problem as a vehicle routing problem with two depots and two types of routes, one for drivers and the other for vehicles. We propose a mixed integer programming formulation for the problem and design a branch-and-cut algorithm to solve it. Computational results show that the proposed approach can find optimal solutions for instances with up to 30 nodes.