Stereotypes have been studied extensively in the fields of social psychology and, especially with the recent advances in technology, in computational linguistics. Stereotypes have also gained even more attention nowadays because of a notable rise in their dissemination due to demographic changes and world events. This paper focuses on ethnic stereotypes related to immigration and presents the StereoHoax corpus, a multilingual dataset of 17,814 tweets in French, Italian, and Spanish. The corpus includes conversational threads reporting on and responding to racial hoaxes about immigrants, which we define as false claims of unlawful actions attributed to specific ethnic groups. This work describes the data collection process and the fine-grained annotation scheme we used, which is based mainly on the Stereotype Content Model adapted to the study applied to immigrants of Bosco et al. (2023). Quantitative and qualitative analyses show the distribution and correlation of annotated categories across languages, revealing, for instance, intercultural differences in the expression of stereotypes through forms of discredit. To validate our data, we performed four machine learning experiments using pre-trained BERT-like models in order to lay a foundation for automatic stereotype detection research. Leveraging the StereoHoax corpus, we gained crucial insights into the importance of context, especially in relation to the detection of implicit stereotypes. Overall, we believe that the StereoHoax corpus will prove to be a valuable resource for the automatic detection of stereotypes regarding immigrants and the study of the linguistic and psychological patterns associated with their dissemination.