The performances of blind source separation (BSS) are still not satisfiable to apply to the real environments. The major obstacle may seem the finite filter length of the assumed mixing model and the nonlinear sensor noises. This paper presents a two-step speech enhancement method with stereo microphone inputs. The first is an ordinary frequency-domain BSS step, and the second is the removal of the remaining cross-channel interference by a spectral cancellation approach using a probabilistic source absence/presence detection technique. Our experimental results show good separation enhancement performances on the real recordings of speech and music signals compared to the conventional BSS methods.