Non-negative tensor factorization has been shown effective for discovering phenotypes from the EHR data with minimal human supervision. In most cases, an interaction tensor of the elements in the EHR (e.g., diagnoses and medications) has to be first established before the factorization can be applied. Such correspondence information however is often missing. While different heuristics can be used to estimate the missing correspondence, any errors introduced will in turn cause inaccuracy for the subsequent phenotype discovery task. This is especially true for patients with multiple diseases diagnosed (e.g., under critical care). To alleviate this limitation, we propose the hidden interaction tensor factorization (HITF) where the diagnosis-medication correspondence and the underlying phenotypes are inferred simultaneously. We formulate it under a Poisson non-negative tensor factorization framework and learn the HITF model via maximum likelihood estimation. For performance evaluation, we applied HITF to the MIMIC III dataset. Our empirical results show that both the phenotypes and the correspondence inferred are clinically meaningful. In addition, the inferred HITF model outperforms a number of state-of-the-art methods for mortality prediction.