We present experimental and numerical investigations of high-energy mid-infrared filamentation with multi-octave-spanning supercontinuum generation (SCG), pumped by a 2.4 μm, 250 fs Cr:ZnSe chirped-pulse laser amplifier. The SCG is demonstrated in both anomalous and normal dispersion regimes with YAG and polycrystalline ZnSe, respectively. The formation of stable and robust single filaments along with the visible-to-mid-infrared SCG is obtained with a pump energy of up to 100 μJ in a 6-mm-long YAG medium. To the best of the authors’ knowledge, this is the highest-energy multi-octave-spanning SCG from a laser filament in a solid. On the other hand, the SCG and even-harmonic generation based on random quasi-phase matching (RQPM) are simultaneously observed from the single filaments in a 6-mm-long polycrystalline ZnSe medium with a pump energy of up to 15 μJ. The numerical simulations based on unidirectional pulse propagation equation and RQPM show excellent agreement with the measured multi-octave-spanning SCG and even-harmonic generation. They also reveal the temporal structure of mid-infrared filaments, such as soliton-like self-compression in YAG and pulse broadening in ZnSe.