Waste management systems are overloaded with huge streams of plastic, a large part of this being originated from packaging. Additionally, the production of wheat, one of the most cultivated crops in the world, generates low-value lignocellulosic materials, which are mostly discarded. In this study, the wheat lignocellulosic byproducts straw and bran were used for the co-production of enzymes and bio-based materials with possible application as packaging via the compression molding method. The mechanical properties of the films were studied based on the effects of the removal of lignin by alkali and biological pretreatment, the growth of filamentous fungi, the size of the particles, and the enzyme recovery. Generally, the straw films were stiffer than the bran ones, but the highest Young’s modulus was obtained for the biologically pretreated bran (1074 MPa). The addition of a step to recover the fungal cellulases produced during the cultivation had no statistical effect on the mechanical properties of the films. Moreover, alkali and biological pretreatments improved the anaerobic biodegradability of the straw films. Thus, the wheat bran and straw can be used for the co-production of enzymes, materials, and biogas, potentially changing how wheat and packaging wastes are managed.