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Ganymede and Callisto are primary targets of ESA.s JUpiter Icy Moon Explorer (JUICE) and NASA.s Europa Clipper missiondoublePoint Callisto will be visited with a total of about 20 flybys. Ganymede will be the first planetary moon to be orbited by a spacecraft (JUICE). Today comma the atmospheres of the two icy moons are only loosely constrained by observations. Oxygen comma the domimant atmospheric species comma is observable only through faint electron-excited emissions comma complicating derivation of reliable neutral gas abundances or distribution due to poorly constrained electron properties. STIS spectral imaging has recently proven to be a sensitive tool for investigating Io and Europa while in transit of JupiterdoublePoint Atmospheres and plume abundances are probed through extinction of the bright Jupiter Ly-alpha background - independently of electron properties. The observing geometry now during HST Cycle 28 provides optimal conditions to also observe Ganymede and Callisto in transit of Jupiter. Both moons have long (>3.5 h) transits near the Ly-alpha-bright equator of the planet comma a condition that is fulfilled only every virgul6 years. We propose to observe Ganymede and Callisto during one transit of Jupiter each with two consecutive HST orbits. The observations will provide the most precise measurements of the H atmospheres and the first ever spatially resolved constraints on atmospheric H2O - from sublimation or outgassing - for the two largest moons of Jupiter. The transit geometry provides the unique opportunity to measure hemispheric differences in the atmospheres comma which likely arise from the moons. surface volatile distributions as known via albedo dichotomies between the trailing and leading sides.