The purpose of these studies was to establish the influence of the microstructural and rheological characteristics of modified bitumen compositions on the strength indicators of asphalt concrete. The effect of additives concentration on the rheological characteristics and microstructure of binary “bitumen–surfactant”, “bitumen-AG-4I”, and ternary “bitumen-AG-4I-AG-4I” systems has been studied. To assess the effect of bitumen dispersion on the physical and mechanical characteristics of modified asphalt concrete samples, the compressive strength value was determined. The following chemicals have been used as additives: the original product AS-1, industrial additive AMDOR-10, and used sealant AG-4I, a product based on polyisobutylene and petroleum oils. At an increased content of AG-4I (C ≥ 1.0 g/dm3) in ternary systems, the contribution of the emerging intermolecular polyisobutylene network to the development of structuring processes increases while the viscous effect of the surfactant AS-1 decreases. It has been established that the minimum size of bee-like bitumen structures (1.66 µm) is recorded with the joint presence of additives in the bitumen, AS-1 at a level of 1.0 g/dm3 and AG-4I at a level of 1.0 g/dm3. Under the same concentration regimes of the ternary bitumen composition, the maximum increase in compressive strength RD was achieved with the smallest size of bee-like structures of modified bitumen.