Two-dimensional electron gas at the anodic oxide-HgTe(110) interface is studied experimentally (by the magnetocapacitance spectroscopy method) and theoretically for carrier surface density up to 6 × 1012 cm-2. The measurements show the population of up to four subbands with well-resolved Rashba spin splitting in the Fourier transforms. The carrier distribution among the electric subbands agrees with the theory. However, the experimental relative differences of occupancies of spin sub-subbands (0.17-0.3) exceed the calculated ones (0.14). This discrepancy indicates an interface contribution to the spin-orbit splitting. The partial capacitance oscillations for different spin branches in the ground subband differ not only in period but also in amplitude. Because of this, the measured effective cyclotron masses in this subband correspond to the theoretical values for the high-energy spin branch whereas in the excited subbands each corresponds to an average over two branches.