In this paper we tackle the practical challenges of searching encrypted multimodal data (i.e., data containing multiple media formats simultaneously), stored in public cloud servers, with reduced information leakage. To this end we propose MuSE, a Multimodal Searchable Encryption scheme that, by combining only standard cryptographic primitives and symmetric-key block ciphers, allows cloud-backed applications to dynamically store, update, and search multimodal datasets with privacy and efficiency guarantees. As searching encrypted data requires a tradeoff between privacy and efficiency, we also propose a variant of MuSE that resorts to partially homomorphic encryption to further reduce information leakage, but at the cost of additional computational overhead. Both schemes are formally proven secure and experimentally evaluated regarding performance and search precision. Experiments with realistic datasets show that our contributions achieve interesting levels of efficiency and privacy, making MuSE particularly suitable for practical application scenarios.