Identifying offensive content in social media is vital to create safe online communities. Several recent studies have addressed this problem by creating datasets for various languages. In this paper, we explore offensive language identification in texts with transliterations and code-mixing, linguistic phenomena common in multilingual societies, and a known challenge for NLP systems. We introduce TB-OLID, a transliterated Bangla offensive language dataset containing 5,000 manually annotated comments. We train and fine-tune machine learning models on TB-OLID, and we evaluate their results on this dataset. Our results show that English pre-trained transformer-based models, such as fBERT and HateBERT achieve the best performance on this dataset.