We analyze the optical, UV, and X-ray microlensing variability of the lensed quasar SDSS J0924+ 0219 using six epochs of Chandra data in two energy bands (spanning 0.4-8.0 keV, or 1-20 keV in the quasar rest frame), 10 epochs of F275W (rest-frame 1089 angstrom) Hubble Space Telescope data, and high-cadence R-band (rest-frame 2770 angstrom) monitoring spanning 11 years. Our joint analysis provides robust constraints on the extent of the X-ray continuum emission region and the projected area of the accretion disk. The best-fit half-light radius of the soft X-ray continuum emission region is between 5 x 10(13) and 10(15) cm, and we find an upper limit of 10(15) cm for the hard X-rays. The best-fit soft-band size is about 13 times smaller than the optical size, and roughly 7GM(BH)/c(2) for a 2.8 x 10(8) M-circle dot black hole, similar to the results for other systems. We find that the UV emitting region falls in between the optical and X-ray emitting regions at 10(14) cm < r(1/2,UV) <3x10(15) cm. Finally, the optical size is significantly larger, by 1.5 sigma, than the theoretical thin-disk estimate based on the observed, magnification-corrected I-band flux, suggesting a shallower temperature profile than expected for a standard disk.