In this work, we present a method and two large-scale datasets for Script-Driven Multimodal Video Summarization. The proposed method, SD-MVSum, builds on our earlier SD-VSum method for script-driven video summarization, which considered just the visual content of the video. SD-MVSum takes into account, in addition to the visual modality, the relevance of the user-provided script with the spoken content (i.e., audio transcript) of the video. The dependence between each considered pair of data modalities, i.e., script-video and script-transcript, is modeled using a new weighted cross-modal attention mechanism. This mechanism explicitly exploits the semantic similarity between the paired modalities in order to promote the parts of the full-length video with the highest relevance to the user-provided script. Furthermore, we extend two large-scale datasets for script-driven (S-VideoXum) and generic (MrHiSum) video summarization, to make them suitable for training and evaluation of script-driven multimodal video summarization methods. Experimental comparisons document the competitiveness of the proposed SD-MVSum method against other SotA approaches for script-driven and generic video summarization. Our new method and extended datasets are available at: https://github.com/IDT-ITI/SD-MVSum.