The presence of large-scale corpora for Natural Language Inference (NLI) has spurred deep learning research in this area, though much of this research has focused solely on monolingual data. Code-mixing is the intertwined usage of multiple languages, and is commonly seen in informal conversations among polyglots. Given the rising importance of dialogue agents, it is imperative that they understand code-mixing, but the scarcity of code-mixed Natural Language Understanding (NLU) datasets has precluded research in this area. The dataset by Khanuja et al. (2020a) for detecting conversational entailment in codemixed Hindi-English text is the first of its kind. We investigate the effectiveness of language modeling, data augmentation, translation, and architectural approaches to address the codemixed, conversational, and low-resource aspects of this dataset. We obtain +8.09% test set accuracy over the current state of the art.