With the rise in accessibility and popularity of various social media platforms, people have started expressing and communicating their ideas, opinions, and interests online. While these platforms are active sources of entertainment and idea-sharing, they also attract hostile and offensive content equally. Identification of hostile posts is an essential and challenging task. In particular, Hindi-English Code-Mixed online posts of conversational nature (which have a hierarchy of posts, comments, and replies) have escalated the challenges. There are two major challenges: (1) the complex structure of Code-Mixed text and (2) filtering the relevant previous context for a given utterance. To overcome these challenges, in this paper, we propose a novel hierarchical neural network architecture to identify hostile posts/comments/replies in online Hindi-English Code-Mixed conversations. We leverage large multilingual pre-trained (mLPT) models like mBERT, XLMR, and MuRIL. The mLPT models provide a rich representation of code-mix text and hierarchical modeling leads to a natural abstraction and selection of the relevant context. The propose model consistently outperformed all the baselines and emerged as a state-of-the-art performing model. We conducted multiple analyses and ablation studies to prove the robustness of the proposed model. © 2022 ACM.