A finite HgTe/CdTe superlattice with different dielectric media on either side of the surfaces is investigated by taking into account the wavefunction overlap between the interface states and plasmons. The unit cell of the finite HgTe/CdTe superlattice consists of two electron-like states and a heavy-hole-like state in HgTe and two light-hole-like states in CdTe. Using the random-phase approximation added with some assumptions, we have studied the density - density correlation function by considering the interface state with the wavefunctions overlapping with the electron-like states, the light-hole-like states and the heavy-hole-like states. We have calculated the collective excitation spectra of the intrasubband and the intersubband for both the bulk plasmons and the surface plasmons as a function of the number of unit cells. The Raman intensities due to bulk and surface plasmons are expressed by the relative value of the mode energy of the plasmons.