This article presents the multimodal BigEarthNet (BigEarthNet-MM) benchmark archive consisting of 590,326 pairs of Sentinel-1 and Sentinel-2 image patches to support deep learning (DL) studies in multimodal, multilabel remote sensing (RS) image retrieval and classification. Each pair of patches in BigEarthNet-MM is annotated with multilabels provided by the CORINE Land Cover (CLC) map of 2018 based on its thematically most detailed level-3 class nomenclature. Our initial research demonstrates that some CLC classes are challenging to accurately describe by considering only (single-date) BigEarthNet-MM images. In this article, we also introduce an alternative class nomenclature as an evolution of the original CLC labels to address this problem. This is achieved by interpreting and arranging the CLC level-3 nomenclature based on the properties of BigEarthNet-MM images in a new nomenclature of 19 classes. In our experiments, we show the potential of BigEarthNet-MM for multimodal, multilabel image retrieval and classification problems by considering several state-of-the-art DL models.