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We present the analysis of five joint XMM-Newton/NuSTAR observations, 20 ks each and separated by 12 days, of the broad-line radio galaxy 3C 382. The data were obtained as part of a campaign performed in September-October 2016 simultaneously with VLBA. The radio data and their relation with the X-ray ones will be discussed in a following paper. The source exhibits a moderate flux variability in the UV/X-ray bands, and a limited spectral variability especially in the soft X-ray band. In agreement with past observations, we find the presence of a warm absorber, an iron K$\alpha$ line with no associated Compton reflection hump, and a variable soft excess well described by a thermal Comptonization component. The data are consistent with a "two-corona" scenario, in which the UV emission and soft excess are produced by a warm ($kT \simeq 0.6$ keV), optically thick ($\tau \simeq 20$) corona consistent with being a slab fully covering a nearly passive accretion disc, while the hard X-ray emission is due to a hot corona intercepting roughly 10 per cent of the soft emission. These results are remarkably similar to those generally found in radio-quiet Seyferts, thus suggesting a common accretion mechanism.