The atomic emission and cavity field spectrum of an atom interacting with two-mode fields in the pair-coherent states are investigated. The results for weak initial fields are presented. The spectral structure is discussed. It is found that the peak position of the atomic emission spectrum and the height of the cavity-field spectrum are both affected by the average photon number and the photon-number difference between the two modes sensitively. The effect of the two field intensity on the peak position of the cavity field spectrum and the height of the atomic emission spectrum are both not obvious. Fixing the photon difference of the two fields, the Rabi splitting will arise in atomic emission spectra with strong initial fields. This is useful in experiment for measurement of the Rabi frequency and the atom-field coupling constant. The cavity-field spectrum structure can be modulated by the photon-number difference of the two fields.