Multipactor discharge is a vacuum surface discharge on dielectrics or metals triggered by a secondary electron emission avalanche (SEEA), posing a threat to the stable operation of electrical and quantum information devices. This paper performs a first-principle model of multipactor discharge developing on a dielectric with realistic microscopic surface morphology, revealing the critical role of microstructures and roughness in multipactor physics, which is often neglected in existing studies. The simulation results indicate that the dielectric surface microstructures suppress the development of SEEA by hindering electron motion, influencing the surface charge and electric field distribution within the surface microstructures. The surface charge is predominantly positive, while negative charge accumulation is observed in part of valleys. Under the combined influence of charges and microstructure, a positive parallel electric field (>1 kV mm−1) forms in the valleys, which facilitates electron deceleration and trapping. Backscattered electrons, with higher mean energies than true secondary electrons, can escape the attraction of surface positive charges and thus do not participate in the subsequent SEEA process. In general, rough dielectrics exhibit lower surface charge density, vertical electron flux, and local gas pressure, all of which contribute to improved surface insulation strength. The model-predicted flashover threshold is in good agreement with the experimental data. This paper provides a deeper understanding of the multipactor discharge mechanism on rough surfaces and a first-principle model for developing multipactor suppression techniques using surface morphology optimization.