We have analyzed the deep Chandra observation (~155 ks) of the Compton Thick Active Galactic Nucleus (CT AGN) ESO 428-G014, to study in detail the morphology of the diffuse X-ray emission in the inner ~500 pc radius region. Comparing different X-ray energy bands we find localized differences in the absorbing column and in the emission processes. Collisional ionization may be prevalent in the area of most intense optical line emission (Halpha and [OIII]). There is a good correspondence between optical line, radio continuum and soft (<3 keV) X-ray features, consistent with simulations of jet/molecular disk interactions. At all energies >3 keV, the extended emission in the central 1.5 (170 pc) radius circumnuclear region amounts to ~70-30% of the contribution of a point source in that area (or 40-25% of the total counts in the region). Within a 5 radius, the contribution from extended emission overcomes that from a nuclear point source in the 3-4 keV band. This extended emission suggests scattering of nuclear photons by dense molecular clouds in the inner galactic disk of ESO 428-G014. Its presence may adversely bias the torus modeling of spectra from X-ray telescopes with inferior angular resolution than Chandra, such as NuSTAR and XMM-Newton.