A comprehensive integrated membrane bioreactor (MBR) model for wastewater treatment is here proposed. The model quantifies the main biological and physical processes. The model describes the biological removal of organic matter, nitrogen and phosphorus including greenhouse gases (carbon dioxide, CO2 and nitrous oxide, N2O). The model takes into account the following main innovative aspects jointly: i. Two-step nitrification process; ii. N2O formation due to ammonia-oxidizing bacteria as a product of the hydroxylamine oxidation (NH2OH) and of the nitrite (NO2-) reduction; iii. Soluble microbial product (SMP) formation/degradation due to microbial growth and endogenous respiration; iv. Interlink between SMP and membrane fouling. The model was calibrated by employing a detailed calibration protocol and data from a University Cape Town (UCT) -MBR pilot plant. The key processes contributing to the N2O formation were properly described (total efficiency related to the calibrated model equal to 0.55). Results suggested that the incomplete hydroxylamine oxidation and the heterotrophic denitrification were the predominant processes influencing the N2O production. The model was able to describe the membrane fouling as demonstrated by the high efficiency (0.92) for the resistance state variable. This result confirms the importance in the modelling approach of considering both biological and physical processes jointly.