Human subjective evaluation is the gold standard to evaluate speech quality optimized for human perception. Perceptual objective metrics serve as a proxy for subjective scores. We have recently developed a non-intrusive speech quality metric called Deep Noise Suppression Mean Opinion Score (DNSMOS) using the scores from ITU-T Rec. P.808 subjective evaluation. The P.808 scores reflect the overall quality of the audio clip. ITU-T Rec. P.835 subjective evaluation framework gives the standalone quality scores of speech and background noise in addition to the overall quality. In this work, we train an objective metric based on P.835 human ratings that outputs 3 scores: i) speech quality (SIG), ii) background noise quality (BAK), and iii) the overall quality (OVRL) of the audio. The developed metric is highly correlated with human ratings, with a Pearson's Correlation Coefficient (PCC)=0.94 for SIG and PCC=0.98 for BAK and OVRL. This is the first non-intrusive P.835 predictor we are aware of. DNSMOS P.835 is made publicly available as an Azure service.