In headset and hearing aid applications, it is of interest to retrieve the user's own voice in a noisy environment, e.g. for telephony applications. To do so, the cross-power spectral density (CPSD) of the interference-plus-noise is required. In this paper, a novel maximum likelihood (ML) estimator of the interference-plus-noise CPSD matrix is proposed. The proposed method is able to estimate the interference-plus-noise CPSD matrix, even during signal regions with own voice activity. The method uses a novel procedure for estimating the interference-plus-noise CPSD matrix by first estimating the interference PSD and afterwards the noise PSD in a maximum likelihood sense. Simulation experiments, where the proposed method is compared to other noise CPSD matrix estimators, show that it performs on par or better than competing methods, particularly, in situation where the interferenceto-noise ratio is large.