Observations performed with CO2 near its critical point onboard sounding rockets show that periodical patterns (bands) develop in a two-phase, liquid-vapor system under tangential vibrations in microgravity conditions. Fluids are slightly below their liquid-vapor critical point where liquid and vapor densities are close, surface tension is low, and they exhibit a scaled, universal behavior. With the increase of vibration amplitude, an instability can develop on the band pattern, leading to the appearance of Faraday waves. Theoretical and numerical investigations of the Faraday instability onset and development are carried out taking into account the interaction between the bands. The critical parameters for the onset of instability are determined. The comparisons between theoretical analysis, two-dimensional direct numerical simulation, and original experimental data show good agreement.