A coating rendering superhydrophobic properties to low-density polyethylene (LDPE) films used in packaging applications was herein generated by means of the electrohydrodynamic processing (EHDP) technique. To this end, electrospun ultrathin poly(ε-caprolactone) (PCL) fibers, followed by electrosprayed nanostructured silica (SiO2) microparticles, were deposited on top of the LDPE film. Various electrospinning and electrospraying times were tested and optimized followed by a thermal post-treatment to provide physical adhesion between the bilayer coating and the LDPE substrate. The morphology, hydrophobicity, permeance to limonene, and thermal stability of the resultant nanostructured coatings were characterized. It was observed that by controlling both the deposition time of the electrospun ultrathin PCL fibers and the electrosprayed SiO2 microparticles, as well as the conditions of the thermal post-treatment, effective superhydrophobic coatings were developed onto the LDPE films. The resultant multilayer presented a hierarchical micro/nanostructured surface with an apparent contact angle of 157° and a sliding angle of 8°. The addition of silica reduced, to some extent, the limonene (aroma) barrier, likely due to the increased surface-to-volume ratio, which allowed permeant sorption to occur but improved the thermal stability of the LDPE/PCL film. As a result, the developed multilayer system of LDPE/PCL/SiO2 has significant potential for use in easy-to-empty packaging applications of high water activity products.