Thunderstorms pose threats to life and property in multiple ways, including lightning, hail, heavy rainfall and strong winds. Since those hazards are all caused by strong convection and processes are closely interconnected, nowcasting them can benefit from the same set of observational data; thus, a common framework for nowcasting different hazards is beneficial. In this presentation, we introduce such a framework in the context of machine learning. We present a neural network that detects spatiotemporal patterns in the input data fields using convolutional and recurrent layers. The network can simultaneously analyze inputs from multiple sources. We apply it to data from the Swiss weather radar network, lightning observations of EUCLID, MSG/SEVIRI satellite imagery, numerical weather forecasts of the Swiss COSMO model and a digital elevation model. Our study area is Switzerland and its surroundings.The model is trained to predict lightning, hail and extreme precipitation with lead times up to 60 min at 5 min time resolution; support for longer lead times is possible. We show that the model is able to infer and predict the motion, growth and decay of thunderstorms without explicit detection and tracking of storm objects. It can also often predict the future occurrence of these hazards before their onset. The predictions are probabilistic, indicating the confidence in the occurrence of the hazard, and can be calibrated to accurately reflect the probability of occurrence. We expect that this will enable more accurate and localized warnings of thunderstorm hazards. The model is validated against Eulerian and Lagrangian persistence. We also analyze the contributions of different data sources to the skill of predicting of each hazard using explainable AI methods.