Despite abundant research outcomes of blind source separation (BSS) in many types of simulated environments, their performances are still not satisfactory to be applied 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 multiple microphone inputs. The first step performs a frequency-domain BSS algorithm to produce multiple outputs without any prior knowledge of the mixed source signals. The second step further removes the remaining cross-channel interference by a spectral cancellation approach using a probabilistic source absence/presence detection technique. The desired primary source is detected every frame of the signal, and the secondary source is estimated in the power spectral domain using the other BSS output as a reference interfering source. Then the estimated secondary source is subtracted to reduce the cross-channel interference. Our experimental results show good separation enhancement performances on the real recordings of speech and music signals compared to the conventional BSS methods.