Ideology detection (ID) is important for gaining insights about peoples’ opinions and stances on our world and society, which can find many applications in politics, economics and social sciences. It is not uncommon that a piece of text can contain descriptions of various issues. It is also widely accepted that a person can take different ideological stances in different facets. However, existing datasets for the ID task only label a text as ideologically left- or right-leaning as a whole, regardless whether the text containing one or more different issues. Moreover, most prior work annotates texts from data resources with known ideological bias through distant supervision approaches, which may result in many false labels. With some theoretical help from social sciences, this work first designs an ideological schema containing five domains and twelve facets for a new multifaceted ideology detection (MID) task to provide a more complete and delicate description of ideology. We construct a MITweet dataset for the MID task, which contains 12,594 English Twitter posts, each annotated with a Relevance and an Ideology label for all twelve facets. We also design and test a few of strong baselines for the MID task under in-topic and cross-topic settings, which can serve as benchmarks for further research.