Roberts, Massoulié and co-authors have introduced and studied a flow level model of Internet congestion control that represents the randomly varying number of flows present in a network where bandwidth is dynamically shared between elastic file transfers. In this paper we consider a generalization of the model to include streaming traffic as well as file transfers, under a fairness assumption that includes TCP-friendliness as a special case. We establish stability, under conditions, for a fluid model of the system. We also assess the impact of each traffic type on the other; file transfers are seen by streaming traffic as reducing the available capacity, whereas for file transfers the presence of streaming traffic amounts to replacing sharp capacity constraints by relaxed constraints. The integration of streaming traffic and file transfers has a stabilizing effect on the variability of the number of flows present in the system.