Further development and commercialization of bulk heterojunction (BHJ) solar cells require the search for novel low-cost materials. The present study addresses the relations between the asphaltenes’ chemical structure and the morphology of the poly(3-hexylthiohene) (P3HT)/asphaltene blends as potential materials for the design of BHJ solar cells. By means of all-atom molecular dynamics simulations, the formation of heterophase morphology is observed for the P3HT-based blends with carboxyl-containing asphaltenes, as well as the aggregation of the asphaltenes into highly ordered stacks. Although the π–π interactions between the polyaromatic cores of the asphaltenes in solutions are sufficient for the molecules to aggregate into ordered stacks, in a blend with a conjugated polymer, additional stabilizing factors are required, such as hydrogen bonding between carboxyl groups. It is found that the asphaltenes’ aliphatic side groups may improve significantly the miscibility between the polymer and the asphaltenes, thereby preventing the formation of heterophase morphology. The results also demonstrate that the carboxyl-containing asphaltenes/P3HT ratio should be at least 1:1, as a decrease in concentration of the asphaltenes leads to the folding of the polymer chains, lower ordering in the polymer phase and the destruction of the interpenetrating 3D structure formed by P3HT and the asphaltene phases. Overall, the results of the present study for the first time reveal the aggregation behavior of the asphaltenes of varying chemical structures in P3HT, as well the influence of their presence and concentration on the polymer phase structure and blend morphology, paving the way for future development of BHJ solar cells based on the conjugated polymer/asphaltene blends.