When containers are transported on synchromodal bookings from their origin to their destination, the transport supplier can decide which combination of trucks, trains, and ships to use. This gives transport suppliers many options to route the container through the synchromodal network. Current literature on the individual routing of containers assumes that the trucks are always available and they do not consider empty truck kilometers. A model which individually routes both containers and trucks through a synchromodal network is presented in this paper. We study the effect of integrating the route of individual trucks and containers, considering costs, emissions, and empty truck kilometers by creating the Integrated Container and Truck (ICTR) model, and comparing it to the existing assumption in literature that trucks are always available when routing the container through a synchromodal network. Numerical experiments on a simulated, synchromodal, hinterland network are used to illustrate the model's potential.