We present ALMA rest-frame 230 GHz continuum and CO(2-1) line observations of the nearby Compton-thick Seyfert galaxy ESO428-G14, with angular resolution 0.7 arcsec (78 pc). We detect CO(2-1) emission from spiral arms and a circum-nuclear ring with 200 pc radius, and from a transverse gas lane with size of $sim100$ pc, which crosses the nucleus and connects the two portions the circumnuclear ring. The molecular gas in the host galaxy is distributed in a rotating disk with intrinsic circular velocity $v_{rot}=135$ km/s, inclination $i=57$ deg, and dynamical mass $M_{dyn }=5times 10^9~rm M_{odot}$ within a radius of $sim 1$ kpc. In the inner 100 pc region CO is distributed in a equatorial bar, whose kinematics is highly perturbed and consistent with an inflow of gas towards the AGN. This inner CO bar overlaps with the most obscured, Compton-thick region seen in X-rays. We derive a column density of $rm N(H_2) approx 2times10^{23}~ cm^{-2}$ in this region, suggesting that molecular gas may contribute significantly to the AGN obscuration. We detect a molecular outflow with a total outflow rate $rm dot M_{of}approx 0.8~M_{odot}/yr$, distributed along a bi-conical structure with size of $700$ pc on both sides of the AGN. The bi-conical outflow is also detected in the $rm H_2$ emission line at 2.12 $mu$m, which traces a warmer nuclear outflow located within 170 pc from the AGN. This suggests that the outflow cools with increasing distance from the AGN. We find that the hard X-ray emitting nuclear region mapped with Chandra is CO-deprived, but filled with warm molecular gas traced by $rm H_2$ - thus confirming that the hard (3-6 keV) continuum and Fe K$alpha$ emission are due to scattering from dense neutral clouds in the ISM.
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