A binaural model predicting speech intelligibility in envelope-modulated noise for normal-hearing (NH) and hearing-impaired listeners is proposed. The study shows the importance of considering an internal noise with two components relying on the individual audiogram and the level of the external stimuli. The model was optimized and verified using speech reception thresholds previously measured in three experiments involving NH and hearing-impaired listeners and sharing common methods. The anechoic target, in front of the listener, was presented simultaneously through headphones with two anechoic noise-vocoded speech maskers (VSs) either co-located with the target or spatially separated using an infinite broadband interaural level difference without crosstalk between ears. In experiment 1, two stationary noise maskers were also tested. In experiment 2, the VSs were presented at different sensation levels to vary audibility. In experiment 3, the effects of realistic interaural time and level differences were also tested. The model was applied to two datasets involving NH listeners to verify its backward compatibility. It was optimized to predict the data, leading to a correlation and mean absolute error between data and predictions above 0.93 and below 1.1 dB, respectively. The different internal noise approaches proposed in the literature to describe hearing impairment are discussed.