The interband cascade laser (ICL) is an ideal candidate for low-power mid-infrared frequency comb spectroscopy. In this work, we demonstrate that its intracavity second-order optical nonlinearity induces a coherent up-conversion of the generated mid-infrared light to the near-infrared through second-harmonic and sum-frequency generation. At 1.8 µm, 10 mW of light at 3.6 µm convert into sub-nanowatt levels of optical power, spread across 30 nm of spectral coverage. The observed linear-to-nonlinear conversion efficiency exceeds ${3\;{\unicode{x00B5} {\rm W/W}}^2}$3µW/W2 in continuous wave operation. We use a dual-band ICL frequency comb source to characterize water vapor absorption in both spectral bands.