This article proposes a mechanism for a significant improvement in the mechanical performance of a simulated waste fraction, composed of an immiscible low-density polyethylene (LDPE) and high-impact polystyrene (HIPS) blend (70:30 proportion), when chemithermomechanical pulp (CTMP) fibers and maleic acid anhydride grafted styrene-ethylene/butylene-styrene block copolymer (MAH-SEBS) were added. SEM micrographs of composites showed an increased contact between the continuous LDPE phase and CTMP fibers when the functionalized compatibilizer (MAH-SEBS) was used. By employing a model study using LDPE and regenerated cellulose, we investigated the interphase properties between the plastic phase and the cellulosic component. The model study utilized ESCA, FTIR, and contact angle analysis to follow the reaction between the cellulose surface and the functionalized compatibilizer. All three methods showed that MAH-SEBS was bonded to the surface of the cellulose. The single-fiber fragmentation test showed that the adhesion between cellulose fibers and the plastic matrix was significantly improved for MAH-SEBS-modified samples. The effect of enhanced adhesion on increased mechanical properties of cellulose composites is also discussed, and a prediction of composite strength given, based on interfacial adhesion promotion and fiber properties.