Using the PACS and SPIRE spectrometers on board Herschel, we obtained observations of the Taffy galaxies (UGC 12914/12915) and bridge. The Taffy system is believed to be the result of a face-on collision between two gas-rich galaxies, in which the stellar disks passed through each other, but the gas was dispersed into a massive H i and molecular bridge between them. Emission is detected and mapped in both galaxies and the bridge in the C ii157.7 m and O i63.2 m fine-structure lines. Additionally, SPIRE FTS spectroscopy detects the C i and C i neutral carbon lines, and weakly detects high-J CO transitions in the bridge. These results indicate that the bridge is composed of a warm multi-phase medium consistent with shock and turbulent heating. Despite low star formation rates in the bridge, the C ii emission appears to be enhanced, reaching C ii/FIR ratios of 3.3% in parts of the bridge. Both the C ii and O i lines show broad intrinsic multi-component profiles, similar to those seen in previous CO (1-0) and H i observations. The C ii emission shares similar line profiles with both the double-peaked H i profiles and shares a high-velocity component with single-peaked CO profiles in the bridge, suggesting that the C ii emission originates in both the neutral and molecular phases. We show that it is feasible that a combination of turbulently heated H2 and high column-density H i, resulting from the galaxy collision, is responsible for the enhanced C ii emission.