Magnetoabsorption in far and mid IR ranges in double HgTe/CdHgTe quantum wells with inverted band structure has been studied in high magnetic fields up to 30 T. Numerous intraband and interband transitions have been revealed in the spectra and interpreted within axial 8 × 8 k·p model. Splitting of dominant magnetoabsorption lines resulting from optical transitions from hole-like zero-mode Landau level has been discovered and discussed in terms of a built-in electric field and collective phenomena.