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The received signal of passive radar based on mobile communication signals contains direct and multipath interference (DMI) signals from multiple co-channel base stations (CCBS). The direct signal spatial spectrum of each CCBS should be obtained first to eliminate the co-channel interference. The performance of the traditional spatial spectrum estimation algorithms based on uniform linear array (ULA) is related to the number of array elements. In the complex co-channel interference environment, the array requires an ultra-large number of array elements and the spatial spectrum estimation resolution is poor. This paper proposes a method for estimating the direct signal spatial spectrum of the CCBS by fusing coprime array and compressive sensing. Firstly, an augmented virtual array signal is constructed by using the second-order statistics of the received signals of the coprime array and then the compressive sensing algorithm is used to estimate the spatial spectrum of the direct signal of the CCBS. The proposed method can achieve higher resolution and higher-degrees-of-freedom (DOFs) performance than traditional ULA by using the same number of array elements. The effectiveness of the proposed method is verified by numerical simulation analysis and experimental data.