Abstract The challenges of food security, water use, energy consumption and the growing global demand for food raise the importance of ensuring sustainability of the food supply chains (FSCs). Studies in relevant literature discuss the sustainability performances of FSCs generally without distinguishing between the internal and external stakeholders’ concerns or clarifying the existence of greenwashing or bluewashing attempts, jeopardising true sustainability. This is why modelling towards some holistic treatment of the problem that satisfies those concerns is required. This paper proposes a framework to evaluate the true sustainability performance of FSCs by considering Triple-Bottom-Line (TBL) indicators, i.e. economic, environmental and social. In light of the proposed framework, two models have been developed, one calculating the internal and the other an external sustainability score. The presented models can handle interval or ordinal qualitative and quantitative indicators concurrently while considering desirable and undesirable factors. These novel models have been implemented on data from fifty FSCs in Istanbul, using a two-stage Imprecise Data Envelopment Analysis (IDEA) with a special multiplier. To facilitate visualisation of true sustainability assessment, an internal-external sustainability performance matrix is proposed. Results reveal that the internal sustainability performance of the focal FSCs is better than the external one. The economic dimension predominates in Turkish FSCs’ internal sustainability performance, while the environmental and social dimensions predominate in the external sustainability performance of the FSCs.