Natural disasters are unavoidable and may lead to serious damage to transportation networks, often resulting in catastrophic losses. Masonry arch bridges (MABs) represent around 40% of the bridge stock in many European railway networks. In Portugal, MABs with larger spans and thinner piers were built during the early 20th century to improve the national network. These larger structures are expected to continue operating as a crucial part of the railway network without elevated maintenance costs. Moreover, some are located in regions with high seismic and flood hazards. The joint effects of these hazards in out-of-plane behavior are often overlooked, and their assessment may lead to identifying possible mitigation needs. The present research presents the vulnerability assessment accounting for the likelihood of both seismic and flood events to occur simultaneously on two large multi-span masonry arch bridges in Portugal. The results show the effects of the loss in stiffness due to asymmetrical scour in the out-of-plane failure mechanism of the masonry arch bridges. Fragility curves are obtained by considering structure-related uncertainties for different levels of intensity given by peak ground acceleration for the seismic hazard and flow discharge for the flood hazard. The resulting vulnerability curves, obtained by employing surrogate models, provide useful information for prioritizing assets considering their exposure to multiple hazards, thus aiding in maintaining the desired performance of the railway network.