Document image classification is different from plain-text document classification and consists of classifying a document by understanding the content and structure of documents such as forms, emails, and other such documents. We show that the only existing dataset for this task (Lewis et al., 2006) has several limitations and we introduce two newly curated multilingual datasets WIKI-DOC and MULTIEURLEX-DOC that overcome these limitations. We further undertake a comprehensive study of popular visually-rich document understanding or Document AI models in previously untested setting in document image classification such as 1) multi-label classification, and 2) zero-shot cross-lingual transfer setup. Experimental results show limitations of multilingual Document AI models on cross-lingual transfer across typologically distant languages. Our datasets and findings open the door for future research into improving Document AI models.