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 0.4-8.0keV, or 1-20keV in the quasar rest frame), 10 epochs of F275W (rest-frame 1089{AA}) Hubble Space Telescope data, and high-cadence R-band (rest-frame 2770{AA}) 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 5x10^13^ 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 2.8x10^8^M_{sun} 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.