Code-switching, the use of more than one language within a single utterance, is ubiquitous in much of the world, but remains a challenge for NLP largely due to the lack of representative data for training models. In this paper, we present a novel model architecture that is trained exclusively on monolingual resources, but can be applied to unseen code-switched text at inference time. The model accomplishes this by jointly maintaining separate word representations for each of the possible languages, or scripts in the case of transliteration, allowing each to contribute to inferences without forcing the model to commit to a language. Experiments on Hindi-English part-of-speech tagging demonstrate that our approach outperforms standard models when training on monolingual text without transliteration, and testing on code-switched text with alternate scripts.