In the last decades, the overuse of synthetic polymers in the packaging industry has become a serious global environmental problem due to their nonbiodegradability. To overcome this issue, attention has been driven to study alternative materials, namely the use of biodegradable biopolymers extracted from agro-industrial residues, as materials for food packages. In this work, the polysaccharide arabinoxylan, previously extracted from corn fibre by alkaline hydrolysis, was used to produce composite and multilayer films. The composite films were produced by casting an oil-in-water emulsion with different quantities of oleic acid, while the multilayer films (beeswax-arabinoxylan-beeswax) were manufactured by submerging the arabinoxylan films in a beeswax solution. Both film types, along with a film composed only of arabinoxylan, were characterised in terms of their antioxidant activity, optical and mechanical properties, surface hydrophobicity, and barrier properties against water vapour (WVP), gases, and ultraviolet-visible (UV-vis) radiation. All the films developed were soluble in water. The multilayer films were more advantageous than the emulsion-based ones due to their enhanced barrier properties against water vapour (WVP = 0.58 × 10−11 mol/m∙s∙Pa), oxygen (with a permeability of 3.28 × 10−12 mol.m−1.s−1.Pa−1) and UV-vis radiation and higher values of water contact angle (92.43°), tensile stress (4.11 MPa), and Young’s modulus (15.96 MPa). The films developed, especially the multilayer ones, showed a good potential to produce flexible packages for low-water-content food products (e.g., several types of nuts).