Machine learning (ML) has become a widespread strategy for studying complex microbiome signatures associated with disease. To this end, metagenomics data are often processed into a single "view" of the microbiome, such as its taxonomic (species) or functional (gene) composition, which in turn serves as input to such ML models. When further omics are available, such as metabolomics, these can be analyzed as additional complementary views. Following training and evaluation, the resulting model can be explored to identify informative features, generating hypotheses regarding underlying mechanisms. Importantly, however, using a single view generally offers relatively limited hypotheses, failing to capture simultaneous shifts or dependencies across multiple microbiome layers that likely play a role in microbiome-host interactions. In this work, inspired by the broad domain of multi-view learning, we constructed an integrated ML analysis pipeline using multiple microbiome views. We specifically aimed to investigate the impact of various integration approaches on the ability to predict disease state based on multiple microbiome-related views, and to generate biological insights. Applying this pipeline to data from 25 case-control metagenomics studies, we found that multi-view models typically result in performances that are comparable to the best-performing single view, yet, provide a mixed set of informative features from different views, while accounting for dependencies and links between them. To further enhance such models, we developed a new framework termed MintTea, based on sparse generalized canonical correlation analysis, to identify multi-view modules of features, highlighting shared trends in the data expressed by the different views. We showed that this framework identified multiple modules that were both highly predictive of the disease state, and exhibited strong within-module associations between features from different views. We accordingly advocate for using multi-view models to capture multifaceted microbiome signatures that likely better reflect the complex mechanisms underlying microbiome-disease associations.