In this paper, we present the longest exposed (97 ks) XMM-Newton EPIC-pn spectrum ever obtained for the Seyfert 1.5 galaxy 1H 0419-577. With the aim of explaining the broadband emission of this source, we took advantage of the simultaneous coverage in the optical/UV that was provided in the present case by the XMM-Newton Optical Monitor and by a HST-COS observation. Archival FUSE flux measurements in the far-ultraviolet were also used for the present analysis. We successfully modeled the X-ray spectrum and the optical/UV fluxes data points using a Comptonization model. We found that a blackbody temperature of T ∼ 56 eV accounts for the optical/UV emission originating in the accretion disk. This temperature serves as an input for the Comptonized components that model the X-ray continuum. Both a warm (T wc ∼ 0.7 keV, τ wc ∼ 7) and a hot corona (T hc ∼ 160 keV, τ hc ∼ 0.5) intervene to upscatter the disk photons to X-ray wavelengths. With the addition of a partially covering (C v ∼ 50%) cold absorber with a variable opacity ( N H ∼ [10 19 −10 22 ] cm −2 ), this model can also explain the historical spectral variability of this source, with the present dataset presenting the lowest one ( N H ∼ 10 19 cm −2 ). We discuss a scenario where the variable absorber becomes less opaque in the highest flux states because it gets ionized in response to the variations of the X-ray continuum. The lower limit for the absorber density derived in this scenario is typical for the broad line region clouds. We infer that 1H 0419-577 may be viewed from an intermediate inclination angle i ≥ 54 • , and, on this basis, we speculate that the X-ray obscuration may be associated with the innermost dust-free region of the obscuring torus. Finally, we critically compare this scenario with all the different models (e.g., disk reflection) that have been used in the past to explain the variability of this source.