The superior mechanical qualities of polyurethane have garnered increasing attention for its application in modifying asphalt mixtures. However, polyurethane needs to use polyols to cure, and polyols need to be produced by petroleum refining. As we all know, petroleum is a non-renewable energy source. In order to reduce oil consumption and conform to the trend of a green economy, lignin and chitin were used instead of polyols as curing agents. In this paper, a biological polyurethane-modified asphalt mixture (BPA-16) was designed and compared with a polyurethane-modified asphalt mixture (PA-16) and a matrix asphalt mixture (MA-16). The viscoelastic characteristics of the three asphalt mixtures were evaluated using dynamic modulus, static modulus, and creep tests. The interplay between dynamic and static modulus and frequency is examined, along with the variations in the correlation between dynamic and static modulus. The creep behavior of the mixture was ultimately examined by a uniaxial static load creep test. The findings indicate that the dynamic modulus of BPA-16 exceeds those of PA-16 and MA-16 by 8.7% and 30.4% at 25 Hz and −20 °C, respectively. At 25 Hz and 50 °C, the phase angle of BPA-16 decreases by 26.3% relative to that of MA-16. Lignin and chitin, when utilized as curing agents in place of polyol, can enhance the mechanical stability of asphalt mixtures at low temperatures and diminish their temperature sensitivity. A bio-based polyurethane-modified asphalt mixture can also maintain better elastic properties in a wider temperature range. At −20–20 °C, the dynamic and static moduli of BPA-16, PA-16 and MA-16 are linear, and they can be converted by formula at different frequencies. The failure stages of BPA-16, PA-16, and MA-16 are not observed during the 3600 s creep duration, with BPA-16 exhibiting the least creep strain, indicating that lignin and chitin enhance the resistance to permanent deformation in PU-modified asphalt mixes.