Code-switching (CS) refers to a linguistic phenomenon where a speaker uses different languages in an utterance or between alternating utterances. In this work, we study end-to-end (E2E) approaches to the Mandarin-English code-switching speech recognition task. We first examine the effectiveness of using data augmentation and byte-pair encoding (BPE) subword units. More importantly, we propose a multitask learning recipe, where a language identification task is explicitly learned in addition to the E2E speech recognition task. Furthermore, we introduce an efficient word vocabulary expansion method for language modeling to alleviate data sparsity issues under the code-switching scenario. Experimental results on the SEAME data, a Mandarin-English code-switching corpus, demonstrate the effectiveness of the proposed methods.