We develop a pulse-based representation of temporal rainfall with multifractal properties in the small-scale limit. The representation combines a traditional model for the exterior process at the synoptic scale with a novel hierarchical pulse model for the event interiors. For validation we apply the model to a temporal rainfall record from Florence, Italy. Although the model has only six parameters (four for the exterior process and two for the event interiors), it accurately reproduces a wide range of empirical statistics, including the distribution of dry and wet periods, the distribution of rainfall intensity up to extreme fractiles, the spectral density, the moment scaling function K(q), and the distribution of the partition coefficients for rainfall disaggregation. The model also reproduces observed deviations of physical rainfall from perfect scaling/multiscaling behavior.