Speech intelligibility (SI) prediction models are a valuable tool for the development of speech processing algorithms for hearing aids or consumer electronics. For the use in realistic environments it is desirable that the SI model is non-intrusive (does not require separate input of original and degraded speech, transcripts or a-priori knowledge about the signals) and does a binaural processing of the audio signals. Most of the existing SI models do not fulfill all of these criteria. In this study, we propose an SI model based on phone probabilities obtained from a deep neural net. The model comprises a binaural enhancement stage for prediction of the speech recognition threshold (SRT) in realistic acoustic scenes. In the first part of the study, SRT predictions in different spatial configurations are compared to the results from normal-hearing listeners. On average, our approach produces lower errors and higher correlations compared to three intrusive baseline models. In the second part, we explore if measures relevant in spatial hearing, i.e., the intelligibility level difference (ILD) and the binaural ILD (BILD), can be predicted with our modeling approach. We also investigate if a language mismatch between training and testing the model plays a role when predicting ILD and BILD. This point is especially important for low-resource languages, where not thousands of hours of language material are available for training. Binaural benefits are predicted by our model with an error of 1.5 dB. This is slightly higher than the error with a competitive baseline MBSTOI (1.1 dB), but does not require separate input of original and degraded speech. We also find that good binaural predictions can be obtained with models that are not specifically trained with the target language.