The development of code-mixing (CM) NLP systems has significantly gained importance in recent times due to an upsurge in the usage of CM data by multilingual speakers. However, this proves to be a challenging task due to the complexities created by the presence of multiple languages together. The complexities get further compounded by the inconsistencies present in the raw data on social media and other platforms. In this paper, we present a neural stack based dependency parser for CM data of Bengali and English by utilizing pre-existing resources for closely related Hindi and English CM treebank as well as monolingual treebanks for Bengali, Hindi and English. To address the issue of scarcity of annotated resources for Bengali-English CM pair, we present a rule based system to computationally generate a synthetic code-mixing treebank for Bengali and English (Syn-BE) which is used to further improve the accuracy of our dependency parser. For evaluation purpose, we present a dataset of 500 Bengali-English tweets annotated under Universal Dependencies scheme.