Images in the J, H and K bands and in the the v=1-0 S(1) line of H2 of the central region of the almost edge-on galaxy NGC 3079 reveal contributions from direct and scattered starlight, emission from hot dust and molecular gas, and extinction gradients. The central 100 pc suffers an extinction of 6 mag. Extremely red near-infrared colours require the presence of hot dust at about 1000 K. Less reddened parts of the bulge require either a 20% J-band contribution from young stars in a stellar bar, or a 20-30% contribution from scattered stellar light. The nucleus is surrounded by a dense molecular disk of radius 300 pc. Emission from H2 and hot dust traces a cavity of radius 120 pc. In the central few hundred pc, HI spin temperatures must be less than 275 K and the CO-to_H2 conversion factor is at most 5% of the standard Galactic value. This is consistent with theoretical predictions for environments subjected to dissociative shocks, where reformation of H2 is impeded by high dust grain temperatures. The overall molecular gas content of NGC 3079 is normal for a late-type galaxy.