To evaluate the thermal stability of composite polymer-modified asphalt, thermoplastic elastomer styrene-butadiene rubber (SBR)/polypropylene (PP) pellets were prepared using a hot-melt blending technique, with butyl rubber powder and waste polypropylene pellets as raw materials. The effects of different evaluation indexes on the thermal stability of SBR/PP-modified asphalt were investigated using a frequency scan test and a multi-stress creep recovery (MSCR) test, and the compatibility of SBR/PP particles with asphalt was studied using the Cole–Cole diagram and microstructure images. The tests show that, firstly, the performance grade (PG) classification of asphalt can be improved by adding an SBR/PP thermoplastic elastomer to enhance the adaptability of asphalt in high- and low-temperature environments, and the evaluation separation index can reflect the high-temperature storage stability of composite-modified asphalt more reasonably. Additionally, the larger the rubber-to-plastic ratio the worse the high-temperature thermal stability of composite-modified asphalt. Moreover, the addition of additives to the composite particles can promote the SBR/PP particles in the asphalt to be more uniformly dispersed, forming a more desirable microstructure and improving the thermal stability of composite-modified asphalt. Ultimately, the semicircular curve of the Cole–Cole diagram can reflect the compatibility characteristics of the two-phase structure of SBR/PP-modified asphalt, which can be used as an auxiliary index to evaluate the compatibility of polymer-modified asphalt.