The stability of a two-layer film flow of non-Newtonian fluids is studied with a linear temporal approach. Shear-thinning fluids are considered, which follow the four-parameter inelastic Carreau model. A modified Orr-Sommerfeld equation system is obtained, which is solved by using a spectral Tau collocation method based on Chebyshev polynomials. The effects of density and viscosity stratification are considered, as well as the influence of the shear-thinning properties of the fluid. It is found that, when the viscosity is stronger in the upper layer, the base flow and the stability properties are almost not influenced by the change of the shear-thinning properties in this upper layer. In the other situations, the shear-thinning properties have an influence on the different instabilities, the long-wave surface instability and the short- and long-wave interface instabilities.