We present ALMA 230 GHz continuum and CO(2-1) observations of the nearby Compton-thick Seyfert galaxy ESO428-G14, with angular resolution 0.'' 7 (78 pc). CO(2-1) is distributed in clumpy spiral arms, a lopsided circumnuclear ring (CNR) with similar to 200 pc radius, and a transverse gas lane with size <100 pc, which crosses the nucleus and connects the two portions of the CNR. The main CO velocity gradient is consistent with a rotating disk with dynamical mass M-dyn = 5 x 10(9) M-circle dot within similar to 1 kpc. We detect off-plane gas motions with respect to the main disk plane which likely trace a molecular outflow with rate (M)over bar(of) approximate to 0.1-0.3 M-circle dot yr(-1), along a biconical structure with radius 700 pc. The CO outflow smoothly joins the warm molecular outflow detected in SINFONI/Very Large Telescope data in the central 170 pc, suggesting that the outflow may cool with increasing distance. Our dynamical modeling of the inner 100 pc region suggests a warped disk or bar, and of fast gas streams which may trace an inflow toward the AGN. The inner warped disk overlaps with the most obscured, CT region seen in X-rays. There, we derive a column density N (H-2) approximate to 2 x 10(23) cm(-2), suggesting that molecular gas may contribute significantly to the AGN obscuration. Most of the hard X-ray emitting nuclear region is deprived of cold molecular gas and shows a CO-cavity. The CO-cavity is filled with warm molecular gas traced by H-2, confirming that the 3-6 keV continuum and Fe K alpha emission are due to scattering from dense ISM clouds.
