Considering the Mooney–Rivlin hyperelastic model, a semi-analytical approach is introduced to analyze the rigid–flexible contact behaviors of an inflated membrane balloon between two plates with various interface conditions. This approach is based on the differential formulation and the coupling property of equilibrium equations are well-solved. In order to verify the reliability of the proposed theoretical model, an experimental test is designed, by which some important contact characteristics and patterns (no-slip condition) are obtained. Two special phenomena are observed for the meridian stretch ratio with different friction coefficients. One is that the intersection points of all curves fall in a small interval and the intersection of any two curves represents the same changing rate of the horizontal ordinate, resulting in the maximum difference. The other is the dividing point, where the stretch ratio decreases on the left of it and increases on the right due to the introduction of friction. These results provide solid guidance and support for our understanding of the rigid-flexible contact behaviors of an inflated membrane balloon.