The effects of the interband coupling on the magnetoplasmons and the single-particle excitations are studied for a two-dimensional electron gas in narrow-gap semiconductor quantum wells. Raman selection rules and scattering configurations for the observation of the spin-flip transitions in the magneto-Raman scattering are achieved. Our results reveal an unambiguous relation between the conduction band structure and the Raman-scattering spectrum in narrow-gap semiconductor quantum wells. The electron cyclotron mass and the effective Land\'e g factor can be directly determined from the dependence of the magneto-Raman spectrum on the filling factor in the Faraday and the Voigt configurations, respectively.