We study hybridization of collective plasmon and Carlson-Goldman-Artemenko-Volkov modes in a hybrid system, consisting of two-dimensional layers of electron gas in the normal state and superconductor, coupled by long-range Coulomb forces. The interaction between these collective modes is not possible in a regular single-layer two-dimensional system since they exist in nonoverlapping domains of dimensionless parameter ωτ, where ω is the external electromagnetic field frequency and τ is electron-scattering time. Thus, in a single-layer structure, these modes are mutually exclusive. However, the coupling may become possible in a hybrid system consisting of two separated in space materials with different properties, in particular, the electron-scattering time. We investigate the electromagnetic power absorption by the hybrid system and reveal the conditions necessary for the hybridization of collective modes.