This paper puts forth an interference mitigation scheme, named signal-aligned network coding (SNC), for both uplink and downlink cloud radio access networks (C-RANs). The base stations (BSs) are connected to a central processor (CP) via digital links with individual limited capacities. The user equipments (UEs) communicate with the CP through BSs serving as relay nodes. We focus on the situation that the digital links have moderate rate constraint. Loosely speaking, the capacities of the digital links and the wireless links are of the same order of magnitude. The SNC scheme strategically aligns the signals by signal alignment (SA) and then decodes the aligned signals by physical-layer network coding (PNC). With the proper designs of the network-coded messages transmitted and the alignment of signals, the SNC scheme significantly mitigates the inter-cell interference. No matter the size of the network, the SNC scheme achieves full degrees of freedom (DoF) asymptotically. For the finite signal-to-noise ratio (SNR) performances, simulation results show that the SNC scheme achieves superior sum-rate than the conventional compute-and-forward scheme in the two-user and the three-user cases, especially in the high SNR regime. Copyright © 2020 IEEE.