In a network, a channel introduces correlations to the parties that aim to establish a communication protocol. We present a framework of nonlocal network coding by exploiting a Bell scenario and show the usefulness of nonlocal and quantum resources in network coding. Two-sender and two-receiver interference channels are considered, for which network coding is characterized by two-input and four-outcome Bell scenarios. It is shown that nonsignaling correlations lead to strictly higher channel capacities than quantum correlations in general. This also holds true for quantum and local correlations: network coding with quantum resources shows a strictly higher channel capacity than local ones. It turns out, however, that more nonlocality does not necessarily imply a higher channel capacity. The framework can be generally applied to network communication protocols.