Developing self-supervised learning (SSL) models that can learn universal and transferable representations of H&E gigapixel whole-slide images (WSIs) is becoming increasingly valuable in computational pathology. These models hold the potential to advance critical tasks such as few-shot classification, slide retrieval, and patient stratification. Existing approaches for slide representation learning extend the principles of SSL from small images (e.g., 224 x 224 patches) to entire slides, usually by aligning two different augmentations (or \emph{views}) of the slide. Yet the resulting representation remains constrained by the limited clinical and biological relevance of the views. Instead, we postulate that slides stained with multiple markers, such as immunohistochemistry or special stains, can be seen as different views of the same tissue and can constitute a rich task-agnostic training signal. To this end, we introduce MADELEINE, a multimodal pretraining strategy for slide representation learning. MADELEINE is trained with a dual global-local cross-stain alignment objective on large cohorts of breast cancer samples (N=4,211 WSIs across five stains) and kidney transplant samples (N=12,070 WSIs across four stains). We demonstrate the superior quality of slide representations learned by MADELEINE on various downstream evaluations, ranging from morphological and molecular classification to prognostic prediction, on a total of 21 tasks using 7,299 WSIs from multiple medical centers. Code will be released upon acceptance.