Supporting chefs with ingredient recommender systems to create new recipes is challenging, as good ingredient combinations depend on many factors like taste, smell, cuisine style, texture among others. There have been few attempts to address these issues using machine learning... Importantly, useful models do obviously need to be accurate but importantly -- especially for food professionals -- interpretable. In order to address these issues, we propose the Interpretable Relational Representation Model (IRRM). The main component of the model is a key-value memory network to represent relationships of ingredients. We propose and test two variants of the model. One can learn latent relational representations over a trainable memory network (Implicit model), and the other can learn explainable relational representations over a pre-trained memory network that integrates an external knowledge base (Explicit model). The relational representations resulting from the model are interpretable -- they allow to inspect why certain ingredient pairings have been suggested. The Explicit model additionally allows to integrate any number of manually specified constraints. We conduct experiments on two recipe datasets, including CulinaryDB with 45,772 recipes and Flavornet with 55,001 recipes, respectively. The experimental results show that our models are both predictive and informative. (read more)