Quasi-ordered moth-eye arrays were fabricated in Si using a colloidal lithography method to achieve highly efficient, omni-directional transmission of mid and far infrared (IR) radiation. The effect of structure height and aspect ratio on transmittance and scattering was explored experimentally and modeled quantitatively using effective medium theory. The highest aspect ratio structures (AR = 9.4) achieved peak transmittance of 98%, with >85% transmission for λ = 7-30 μm. A detailed photon balance was constructed by measuring transmission, forward scattering, specular reflection and diffuse reflection to quantify optical losses due to near-field effects. In addition, angle-dependent transmission measurements showed that moth-eye structures provide superior anti-reflective properties compared to unstructured interfaces over a wide angular range (0-60° incidence). The colloidal lithography method presented here is scalable and substrate-independent, providing a general approach to realize moth-eye structures and anti-reflection in many IR-compatible material systems.