A binaural model is proposed to predict speech intelligibility in rooms for normal-hearing (NH) and hearing-impaired listener groups, combining the advantages of two existing models. The leclere2015 model takes binaural room impulse responses (BRIRs) as inputs and accounts for the temporal smearing of the speech by reverberation, but only works with stationary noises for NH listeners. The vicente2020 model takes the speech and noise signals at the ears as well as the listener audiogram as inputs and accounts for modulations in the noise and hearing loss, but cannot predict the temporal smearing of the speech by reverberation. The new model takes the audiogram, BRIRs and ear signals as inputs to account for the temporal smearing of the speech, the masker modulations and hearing loss. It gave accurate predictions for speech reception thresholds measured in seven experiments. The proposed model can do predictions that neither of the two original models can make when the target speech is influenced by reverberation and the noise has modulations and/or the listeners have hearing loss. In terms of model parameters, four methods were compared to separate the early and late reverberation, and two methods were compared to account for hearing loss.