The nonlinear transmission properties of hydrogenated amorphous silicon (a-Si:H) core fibers are characterized from the near-infrared up to the edge of the mid-infrared regime. The results show that this material exhibits linear losses on the order of a few dB/cm, or less, over the entire wavelength range, decreasing down to a value of 0.29 dB/cm at 2.7μm, and negligible nonlinear losses beyond the two-photon absorption (TPA) edge ~ 1.7μm. By measuring the dispersion of the nonlinear Kerr and TPA parameters we have found that the nonlinear figure of merit (FOM(NL)) increases dramatically over this region, with FOM(NL) > 20 around 2μm and above. This characterization demonstrates the potential for a-Si:H fibers and waveguides to find use in nonlinear applications extending beyond telecoms and into the mid-infrared regime.