The present engineering practices show the potential that epoxy asphalt composites (EACs) would be a better choice to obtain long life for busy roads. To understand the service performance–related thermorheological properties of prepared bimodal anhydrides-cured rubber-like EACs (REACs), a direct tensile tester, dynamic shear rheometer and mathematical model were used. Tensile tests demonstrate that all the REACs reported here are more flexible than previously reported anhydrides-cured REACs at both 20 and 0 °C. The better flexibility is attributed to the change of bimodal networks, in which cross-linked short chains decreased and cross-linked long chains increased, relatively. Strain sweeps show that all the REACs have linear viscoelastic (LVE) properties when their strains are smaller than 1.0% from −35 to 120 °C. Temperature sweeps illustrate that the thermorheological properties of REACs evolve from thermosetting to quasi-thermosetting with asphalt content, and all the REACs retain solid state and show elastic properties in the experimental temperature range. A Cole–Cole plot and Black diagram indicate that all the REACs are thermorheologically simple materials, and the master curves were constructed and well-fitted by the Generalized Logistic Sigmoidal models. This research provides a facile approach to tune the thermorheological properties of the REACs, and the cheaper quasi-thermosetting REAC facilitates their advanced applications.