We present the results from an analysis of deep Herschel far-infrared (far-IR) observations of the edge-on disc galaxy NGC 3079. The point spread function-cleaned Photodetector Array Camera and Spectrometer (PACS) images at 100 and 160 μm display a 25 × 25 kpc2 X-shape structure centred on the nucleus that is similar in extent and orientation to that seen in H α, X-rays, and the far-ultraviolet. One of the dusty filaments making up this structure is detected in the Spectral and Photometric Imaging Receiver 250 μm map out to ∼25 kpc from the nucleus. The match between the far-IR filaments and those detected at other wavelengths suggests that the dusty material has been lifted out of the disc by the same large-scale galactic wind that has produced the other structures in this object. A closer look at the central 10 × 10 kpc2 region provides additional support for this scenario. The dust temperatures traced by the 100-160 μm flux ratios in this region are enhanced within a biconical region centred on the active galactic nucleus, aligned along the minor axis of the galaxy, and coincident with the well-known double-lobed cm-wave radio structure and H α-X-ray nuclear superbubbles. PACS imaging spectroscopy of the inner 6 kpc region reveals broad [C ii] 158 μm emission line profiles and OH 79 μm absorption features along the minor axis of the galaxy with widths well in excess of those expected from beam smearing of the disc rotational motion. This provides compelling evidence that the cool material traced by the [C ii] and OH features directly interacts with the nuclear ionized and relativistic outflows traced by the H α, X-ray, and radio emission.