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The states of charge carriers in the spherical InP/InAs/InP core/shell/shell heterostructure are considered. Consideration was carried out for the case of "moderate" quantization, when the energy of electrostatic interaction of an electron and hole is comparable to the energy of their size quantization in an InAs layer. The analytical form of the electron-hole interaction effective potential for the selected relations between the geometric sizes of the sample is determined. The wave functions and energy levels of charge carriers in the presence of this potential are calculated, too. It is shown that taking into account the electron-hole electrostatic interaction leads to an effective narrowing of the width of the band gap of the sample. The values of this effective narrowing is calculated for different values of the layer thickness. Interband optical absorption and photoluminescence in this heterostructure are also considered. With increase of the layer thickness, the absorption and luminescence peaks are shifted to the low frequency range of the absorbed or emitted light. [ABSTRACT FROM AUTHOR]