The thermal storage stability of polymer-modified asphalt (PMA) is the key to avoid performance attenuation during storage and transportation in pavement engineering. However, phase separation of PMA continuously occurs after long-term thermal storage due to the overlooked influence of the phase interface. Two kinds of carbon nanotubes (CNTs) and styrene-butadiene-styrene triblock copolymer (SBS) were selected in this paper to address the aforementioned issue. The segregation test was used to simulate the long-term storage process from 0 to 10 days. Macroperformance included the softening point difference (△SP), irrecoverable compliance (Jnr), recovery rate (R%), and complex modulus (G∗) measured by the softening point test, multistress creep recovery (MSCR) test, and small strain oscillatory rheological test. Microcharacteristics were obtained by the SBS characteristic peak index, SBS-rich phase distribution, polymer swelling degree, and particle characteristics of the SBS-rich phase. They were measured by Fourier-transformed infrared spectroscopy (FT-IR), fluorescence microscopy (FM), and atomic force microscopy (AFM), respectively. Results showed that the optimum CNT amount necessary to obtain an improved thermal storage stability of PMA was 0.5 wt.%. After 10 days of storage, the largest R% of SBS modified asphalt (SBSMA) decreased to 2.24% and the smallest Jnr increased to 0.069 1/kPa, while R% of SBSMA with CNTs was 62.15% and its Jnr was 0.013 1/kPa. R% and Jnr of SBSMA with CNTs showed almost no change after 6 days of storage, implying an effective antirutting performance. The results from the microperformance investigation showed that phase separation of SBS mainly occurred on day 4, while SBS degradation and base asphalt aging led to the worse macroperformance after 10 days of storage. Additional CNTs restrained the SBS-rich phase from floating upward. Meanwhile, a small size of polymer-rich phase and dense network of SBSMA with CNTs were observed in fluorescence microscopy and atomic force microscopy images, thereby exhibiting improved thermal storage stability. Adding CNTs would retard the segregation due to CNT entanglement with SBS.