Anaerobic co-digestion allows for under-utilised digesters to increase biomethane production. The organic fraction of municipal solid waste (OFMSW), i.e., food waste, is an abundant substrate with high degradability and gas potential. This paper investigates the co-digestion of mixed sludge from wastewater treatment plants and OFMSW, through batch and continuous labscale experiments, modelling, and microbial population analysis. The results show a rapid adaptation of the process, and an increase of the biomethane production by 20% to 40%, when codigesting mixed sludge with OFMSW at a ratio of 1:1, based on the volatile solids (VS) content. The introduction of OFMSW also has an impact on the microbial community. With 50% co-substrate and constant loading conditions (1 kg VS/m3/d) the methanogenic activity increases and adapts towards acetate degradation, while the community in the reference reactor, without a co-substrate, remains unaffected. An elevated load (2 kg VS/m3/d) increases the methanogenic activity in both reactors, but the composition of the methanogenic population remains constant for the reference reactor. The modelling shows that ammonium inhibition increases at elevated organic loads, and that intermittent feeding causes fluctuations in the digester performance, due to varying inhibition. The paper demonstrates how modelling can be used for designing feed strategies and experimental setups for anaerobic co-digestion.