A wideband spectrum compressive sensing approach for sparse multiband signals utilizing photonic multi-coset sampling (MCS) is presented. The method employs dual low-rate optical pulses, initially modulated by separate pseudo-random binary sequences (PRBSs), which are then multiplexed to achieve the desired multi-coset pattern. It results in a substantial reduction of the rate requirements for both the sampling optical pulses and PRBSs, leading to a significant enhancement of system bandwidth. In simulations, an instantaneous system bandwidth of 21 GHz is achieved at a low mean sampling rate of 4.8 GS/s, employing two optical pulses with rates of 8.4 GHz and 6 GHz, respectively. The spectra of a mixed signal with six passbands are accurately identified, illustrating the capability of the scheme to recognize the spectra of various types of multiband signals. Furthermore, a comparative analysis of the performance between our proposed scheme and traditional MCS techniques is conducted.