This paper presents a novel noise suppression method to enhance soft speech recorded with a special body-conductive microphone called nonaudible murmur (NAM) microphone. NAM microphone is capable of detecting extremely soft speech, but the recorded soft speech easily suffers from external noise due to its faint volume. To effectively suppress noise on the body-conducted signals, an external noise monitoring framework using an air-conducive microphone has been proposed. In this study, we propose a noise suppression method for this framework based on a probabilistic observation model robust against phase variations. In the proposed method, noise suppression process is formulated as a special case of non-negative tensor factorization of the observed air- and body-conducted signals. Experimental results demonstrate that 1) the proposed method consistently outperforms the conventional method under real noisy environments and 2) the proposed method effectively deals with speech acoustic changes caused by the Lombard reflex.