Besides reducing undesired noise sources and limiting speech distortion, another important objective of a binaural noise reduction algorithm is the preservation of the binaural cues of all sound sources in the acoustic scene. In this paper, we consider the binaural minimum variance distortionless response beamformer with partial noise estimation (BMVDR-N), which allows to trade off between noise reduction performance and binaural cue preservation of the noise component by mixing the output signals of the BMVDR beamformer with the noisy reference microphone signals. For a directional noise source, it has been shown that incorporating an external microphone in addition to the head-mounted microphones enables both the noise reduction performance as well as the interaural time and level difference cues of the noise component to be improved in the output signals. In this paper, we consider an arbitrary noise field and analytically show that incorporating an external microphone in the BMVDR-N beamformer enables 1) a larger output signal-to-noise ratio (SNR) for the same mixing parameter, 2) the same output SNR for a larger mixing parameter, and 3) the same desired output magnitude squared coherence (MSC) of the noise component for a smaller mixing parameter to be obtained. The derived analytical expressions are firstly validated using simulated anechoic acoustic transfer functions, where the listener’s head is modelled as a rigid sphere. Experimental results using recorded signals for a binaural hearing device setup in a reverberant environment also show that in a realistic scenario incorporating an external microphone in the BMVDR-N beamformer significantly improves the output SNR and reduces the mixing parameter that is required to obtain a desired output MSC of the noise component compared to using only the head-mounted microphones.