For the rotating machinery system, it is a challenge to explore fault detection and diagnosis for multiple-faults condition, which simultaneously contains faulty bearing components and faulty gear components. In the study, a fault feature separation and extraction approach is proposed for the bearing-gear fault condition through combining empirical mode decomposition (EMD), Hilbert transform (HT), principal component analysis (PCA), independent component analysis (ICA) techniques. Firstly, EMD is implemented to decompose the single sensor signal to obtain multiple sub-band signals termed as the intrinsic mode functions (IMFs). Secondly, the most relevant IMFs to bearing and gear fault features are selected to construct multiple-channels model with the help of the simulated bearing and gear fault signals. Thirdly, HT is utilized to compute marginal Hilbert spectrum (MHS) for each IMF in multiple-channels model, to construct an MHS matrix. Finally, some statistically independent components are obtained by decomposing the MHS matrix with PCA and ICA, and multiple fault features are identified from these components. The experimental application of the proposed method is put into a bearing-belt-gearbox union machinery system to evaluate its validity. The experimental analysis results indicate that the proposed method is effective to separate and extract a bearing fault and a gear fault for two types of compound bearing-gear fault conditions.