The packet is the fundamental unit of transportation in modern communication networks such as the Internet. Physical layer scheduling decisions are made at the level of packets, and packet-level models with exogenous arrival processes have long been employed to study network performance, as well as design scheduling policies that more efficiently utilize network resources. On the other hand, a user of the network is more concerned with end-to-end bandwidth, which is allocated through congestion control policies such as TCP. Utility-based flow-level models have played an important role in understanding congestion control protocols. In summary, these two classes of models have provided separate insights for flow-level and packet-level dynamics of a network. In this paper, we wish to study these two dynamics together. We propose a joint flow-level and packet-level stochastic model for the dynamics of a network, and an associated policy for congestion control and packet scheduling that is based on alpha-weighted policies from the literature. We provide a fluid analysis for the model that establishes the throughput optimality of the proposed policy, thus validating prior insights based on separate packet-level and flow-level models. By analyzing a critically scaled fluid model under the proposed policy, we provide constant factor performance bounds on the delay performance and characterize the invariant states of the system.