This paper investigates a non-linear mapping approach to extract robust features for ASR and separation of overlapping speech. Based on our previous studies, we continue to use two additional sound sources, namely, from the target and interfering speakers. The focues of this work are: 1) We investigate the feature mapping between different domains with the consideration of MMSE criterion and regression optimizations, demonstrating the mapping of log mel-filterbank energies to MFCC can be exploited to improve the effectiveness of the regression; 2) We investigate the data-driven filtering for the speech separation by using the mapping method, which can be viewed as a generalized log spectral subtraction and results in better separation performance. We demonstrate the effectiveness of the proposed approach through extensive evaluations on the MONC corpus, which includes both non-overlapping single speaker and overlapping multi-speaker conditions.