The pursuit of durable and sustainable pavements has increased interest in alternative asphalt binders, such as biobinders. Their application requires precise rheological characterization to ensure adequate thermal performance and resistance to permanent deformation comparable to conventional binders and polymer-modified bitumens (PMBs). This study analyzed five binders: three conventional penetration grades, one PMB, and a biobinder derived from paper-industry by-products and modified with Styrene–Butadiene–Styrene (SBS) polymer. The ElaStiLe protocol, an extended Multiple Stress Creep and Recovery (MSCR) test, was used to evaluate permanent deformation and thermal susceptibility. At 45 ℃, the biobinder exhibited low non-recovered strain and high recovered strain, indicating satisfactory elastic behavior comparable to the PMB. At 70 ℃, however, the biobinder showed a pronounced reduction in recovery and an increase in deformation, reflecting high temperature susceptibility, while the PMB maintained a more stable viscoelastic response. These results demonstrate that the biobinder provides satisfactory performance at intermediate temperatures but remains sensitive under elevated temperature and stress conditions. The ElaStiLe protocol proved to be an effective tool for identifying thermal instability and assessing the viscoelastic behavior of binders, supporting future research on the performance and durability of alternative and modified binders.