Code-mixing (CM) is a frequently observed phenomenon that uses multiple languages in an utterance or sentence. There are no strict grammatical constraints observed in code-mixing, and it consists of non-standard variations of spelling. The linguistic complexity resulting from the above factors made the computational analysis of the code-mixed language a challenging task. Language identification (LI) and part of speech (POS) tagging are the fundamental steps that help analyze the structure of the code-mixed text. Often, the LI and POS tagging tasks are interdependent in the code-mixing scenario. We project the problem of dealing with multilingualism and grammatical structure while analyzing the code-mixed sentence as a joint learning task. In this paper, we jointly train and optimize language detection and part of speech tagging models in the code-mixed scenario. We used a Transformer with convolutional neural network architecture. We train a joint learning method by combining POS tagging and LI models on code-mixed social media text obtained from the ICON shared task.