A study is conducted on the influence of radio frequency (rf) waves upon interchange stability in HANBIT mirror plasmas. An emphasis is put on the interchange stability near the resonance region, ω0 ≃ Ωi, where ω0 (Ωi) is the angular frequency of the applied rf wave (ion cyclotron frequency). A strong nonlinear interaction between the rf wave and the interchange mode has been observed with the generation of sideband waves. A theory of rf-interchange mode interaction keeping effects of both the equilibrium ponderomotive force and the nonlinear sideband wave coupling is applied to interpret HANBIT experimental results, resulting in good agreement. Results have shown that the nonlinear coupling process is responsible for the rf stabilization of interchange modes near the resonance region.