A model is presented that predicts the binaural advantage to speech intelligibility by analyzing the right and left recordings at the two ears containing mixed target and interferer signals. This auditory-inspired model implements an equalization-cancellation stage to predict the binaural unmasking (BU) component, in conjunction with a modulation-frequency estimation block to estimate the "better ear" effect (BE) component of the binaural advantage. The model's performance was compared to experimental data obtained under anechoic and reverberant conditions using a single speech-shaped noise interferer paradigm. The internal BU and BE components were compared to those of the speech intelligibility model recently proposed by Lavandier et al. [J. Acoust. Soc. Am. 131, 218-231 (2012)], which requires separate inputs for target and interferer. The data indicate that the proposed model provides comparably good predictions from a mixed-signals input under both anechoic and reverberant conditions.