Reprocessed X-ray emission in Active Galactic Nuclei (AGN) can provide fundamental information about the circumnuclear environments of supermassive black holes. Recent mid-infrared studies have shown evidence of an extended dusty structure perpendicular to the torus plane. In this work, we build a self-consistent X-ray model for the Circinus Galaxy including the different physical components observed at different wavelengths and needed to reproduce both the morphological and spectral properties of this object in the mid-infrared. The model consists of four components: the accretion disk, the broad line region (BLR), a flared disk in the equatorial plane and a hollow cone in the polar direction. Our final model reproduces well the 3-70 keV Chandra and NuSTAR spectra of Circinus, including the complex Fe K𝛼 zone and the spectral curvature, although several additional Gaussian lines, associated to either ionized iron or to broadened Fe K𝛼/K𝛽 lines, are needed. We find that the flared disk is Compton thick (𝑁 H,d = 1.01 +0.03 −0.24 × 10 25 cm −2 ) and geometrically thick (𝐶𝐹 = 0.55 +0.01 −0.05 ), and that the hollow cone has a Compton-thin column density (𝑁 H,c = 2.18 +0.47 −0.43 × 10 23 cm −2 ), which is consistent with the values inferred by mid-infrared studies. Including also the BLR, the effective line of sight column density is 𝑁 H = 1.47 +0.03 −0.24 × 10 25 cm −2 . This approach to X-ray modelling, i.e. including all the different reprocessing structures, will be very important to fully exploit data from future X-ray missions.