As the market for polyethylene consumption continues to expand, the amount of waste polyethylene is also increasing. Modifying asphalt with waste polyethylene (PE) is economical and environmentally friendly. The low-temperature performance and storage stability of PE-modified asphalt has long been an insurmountable problem. The high vinyl acetate (VA) content of ethylene–vinyl acetate (EVA) and PE blended into asphalt can improve the compatibility of PE and asphalt. It compensates for the high VA content of EVA brought about by the lack of high-temperature resistance to permanent deformation but is still not conducive to the stable storage of PE at high temperatures. The effect of furfural extraction oil, a crosslinking (DCP) agent, a silicone coupling agent (KH-570), and calcium carbonate (CaCO3) on the rheological properties and compatibility of PE/EVA-modified asphalt was investigated in this study. The conventional physical properties of PE/EVA-modified asphalt were tested after introducing furfural extraction oil, DCP, KH570, and CaCO3to determine the correlations of these materials. In addition, frequency sweep, multiple stress creep and recovery (MSCR), and linear amplitude sweep (LAS) were utilized to characterize the rheological properties and fatigue behavior. The results reveal that the addition of suitable ratios of furfural extract oil, DCP, KH-570, and CaCO3to PE/EVA-modified asphalt produces a remarkable improvement in the viscoelastic characteristics and viscosity compared with PE/EVA-modified asphalt. Furthermore, fluorescence microscopy (FM) was utilized to evaluate the modification mechanism, which shows that PE/EVA undergoes significant crosslinking in asphalt, forming a three-dimensional network structure that dissolves in the asphalt. The storage stability of the PE-modified bitumen was fully determined, and its high-temperature rheology was substantially improved.