Estimating an individual's potential response to interventions from observational data is of high practical relevance for many domains, such as healthcare, public policy or economics. In this setting, it is often the case that combinations of interventions may be applied simultaneously, for example, multiple prescriptions in healthcare or different fiscal and monetary measures in economics. However, existing methods for counterfactual inference are limited to settings in which actions are not used simultaneously. Here, we present Neural Counterfactual Relation Estimation (NCoRE), a new method for learning counterfactual representations in the combination treatment setting that explicitly models cross-treatment interactions. NCoRE is based on a novel branched conditional neural representation that includes learnt treatment interaction modulators to infer the potential causal generative process underlying the combination of multiple treatments. Our experiments show that NCoRE significantly outperforms existing state-of-the-art methods for counterfactual treatment effect estimation that do not account for the effects of combining multiple treatments across several synthetic, semi-synthetic and real-world benchmarks.