We report on even and odd harmonics-enhanced supercontinuum generation in polycrystalline ZnS and ZnSe samples, as pumped by femtosecond mid-infrared pulses. We demonstrate that efficient generation of multiple harmonics takes place due to random quasi-phase matching, which is an intrinsic property of polycrystalline structure that supports multiple simultaneous three-wave mixing processes over a broad wavelength range. More specifically, using sub-mu J, 60 fs, 3.6 mu m input pulses, we measured multi-octave supercontinuum spectra spanning the 0.4-5 mu m and 0.5-5 mu m wavelength ranges in ZnS and ZnSe samples of few mm thickness, respectively. Even and odd harmonics up to the 10th order in ZnS and up to the 8th order in ZnSe were recorded with the input pulses at 4.6 mu m. In contrast, filamentation in ZnTe single crystal is shown to produce only a moderate spectral broadening, which is accompanied by the generation of just second and third harmonics, highlighting the advantages of the polycrystalline structure of zinc-blende semiconductors to generate ultrabroadband radiation. (C) 2018 Optical Society of America