In this work, we present a simple and elegant approach to language modeling for bilingual code-switched text. Since code-switching is a blend of two or more different languages, a standard bilingual language model can be improved upon by using structures of the monolingual language models. We propose a novel technique called dual language models, which involves building two complementary monolingual language models and combining them using a probabilistic model for switching between the two. We evaluate the efficacy of our approach using a conversational Mandarin-English speech corpus. We prove the robustness of our model by showing significant improvements in perplexity measures over the standard bilingual language model without the use of any external information. Similar consistent improvements are also reflected in automatic speech recognition error rates.