Malicious email attachments are a growing delivery vector for malware. While machine learning has been successfully applied to portable executable (PE) malware detection, we ask, can we extend similar approaches to detect malware across heterogeneous file types commonly found in email attachments? In this paper, we explore the feasibility of applying machine learning as a static countermeasure to detect several types of malicious email attachments including Microsoft Office documents and Zip archives. To this end, we collected a dataset of over 5 million malicious/benign Microsoft Office documents from VirusTotal for evaluation as well as a dataset of benign Microsoft Office documents from the Common Crawl corpus, which we use to provide more realistic estimates of thresholds for false positive rates on in-the-wild data. We also collected a dataset of approximately 500k malicious/benign Zip archives, which we scraped using the VirusTotal service, on which we performed a separate evaluation. We analyze predictive performance of several classifiers on each of the VirusTotal datasets using a 70/30 train/test split on first seen time, evaluating feature and classifier types that have been applied successfully in commercial antimalware products and R&D contexts. Using deep neural networks and gradient boosted decision trees, we are able to obtain ROC curves with > 0.99 AUC on both Microsoft Office document and Zip archive datasets. Discussion of deployment viability in various antimalware contexts is provided.