The frequency-comb structure in the extreme ultraviolet (XUV) and vacuum ultraviolet (VUV) regions can be realized by the high-order harmonic generation (HHG) process driven by frequency-comb fields,providing an alteative approach for the measurement of an unknown frequency in XUV or VUV.We consider the case of two driving frequency-comb fields with the same repetition frequency and the carrier frequencies of fundamental-and third-harmonics,respectively.The many-mode Floquet theorem (MMFT) is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and the frequency-comb laser fields.Multiphoton transition paths involving both fundamentaland third-harmonic photons are opened due to the coupling of the third-harmonic frequency-comb field.The multiphoton transition paths are superpositioned when the carrier-envelope-phase shifts (CEPs) fulfill the matching condition.And the interference of the multiphoton transition paths can be controlled by tuning the relative envelope delay between the fields.We find that the quasienergy structure,as well as the multiphoton resonant high-order harmonic generation (HHG) spectra,driven by the two frequency-comb fields can be coherently controlled via the interference of multiphoton transition paths.It is also found that the spectral intensities of the generated harmonics can be modulated,and the modulation behavior is harmonic-sensitive.