To investigate the feasibility of composite modification techniques in improving the performance of recycled asphalt mixtures, in this study, the high-viscosity agent (HVA) and crumb-rubber materials (CRM) were used to modify asphalt with a styrene-butadiene-styrene block copolymer (SBS), in order to prepare SBS-HVA and SBS-CRM composite-modified asphalts. The virgin asphalt mixtures, as well as three asphalt types of recycled asphalt mixtures with 50% reclaimed asphalt pavement (RAP) content, were designed. The optimal asphalt content of the four types of asphalt mixtures was analyzed, and the rutting test, the asphalt bond strength test, the moisture-induced sensitivity test, and the low-temperature cracking resistance test were conducted to investigate the performance of the four types of asphalt mixtures. The results showed that the higher the asphalt kinematic viscosity, the higher the optimum asphalt content of the asphalt mixtures under the same air voids. HVA significantly improves the adhesion between SBS-modified asphalt and aggregate under dry conditions, while SBS-CRM composite-modified asphalt performs similarly to SBS-modified asphalt. Before and after water immersion, the degree of pull-out strength decay between the asphalts and aggregates follows the sequence of SBS-CRM- > SBS- > SBS-HVA-modified asphalts. Additionally, the residual pull-out work follows the sequence of SBS-HVA- > SBS-CRM- > SBS-modified asphalt. SBS-CRM composite-modified asphalt can significantly improve the moisture sensitivity of recycled asphalt mixtures, as well as low-temperature cracking resistance, while SBS-CRM composite-modified asphalt only improves the low-temperature cracking resistance of recycled asphalt mixtures, and does not improve the moisture sensitivity. Based on the results, it is recommended to select the appropriate composite modification method based on the climate and loading conditions, to maximize the value of asphalt, and to achieve sustainable and durable pavement.