The states of double acceptors in HgTe/СdHgTe heterostructures containing quantum wells are theoretically investigated taking into account the substantial difference in the values of the permittivities of the barrier and quantum-well layers. The effect of such a difference and the charge induced at the heterointerfaces arising from it are described with the image-charge potential. Calculation shows a significant change in the binding energy of the acceptor centers—mercury vacancies due to the induced charge; the ionization energies of mercury vacancies are in good agreement with the position of the spectral features in the photoluminescence spectrum of the HgTe/CdHgTe heterostructures containing quantum wells.