Shared autonomous electric vehicles (AEVs) and Electric Vertical-Takeoff-and-Landing (eVTOL) vehicles represent innovative alternatives for sustainable urban mobility. This study explores an integrated optimization problem for systems incorporating both AEVs and eVTOLs, focusing on long-term infrastructure planning—including the sizing and configurations of charging and vertiport facilities—and short-term operational decisions such as vehicle assignment, relocation, and charging. We develop a two-stage stochastic integer program to address the demand uncertainty, featuring an event-activity space-time-battery network that tracks charging options and battery states, thereby facilitating optimal operational choices. To manage the extensive scenario analysis required by the stochastic program, we employ a sample average approximation for sampling and propose an accelerated two-phase Benders decomposition-based algorithm for efficient problem solving. The efficacy of our modeling and algorithmic approach will be validated through extensive testing on a large-scale scenario. Results will demonstrate if integrating both normal- and fast-charging infrastructures for AEVs and appropriate facilities for eVTOLs significantly enhances system profitability and operational efficiency.