The mathematical modeling and analysis for the apparent permeability of shale oil with complicated compositions in dual-wettability shales (superior to existing single-component or single-wettability analysis), which is the core of this work, will help understand the detailed contributions of the considered mechanisms. Based on a previously established flow enhancement model, the effects of the mixed wettability and those triggered by asphaltenes, namely, the wettability alteration, the pore radius reduction, and the viscosity increment, are taken into account by respective corrections of the variables in the model. The effect of the mixed wettability is quantified by the water-wet area ratio, while the surface coverage, the adsorption thickness, and the volume fraction in the free phase are utilized to quantify the effects of asphaltenes. The volume fraction of asphaltenes in the free phase is related to that in both phases by the volume conservation equation. The full mathematical model and its several simplifications are achieved. Comprehensive sensitivity analysis and comparisons are carried out to demonstrate the effects of each variable (i.e., the pore radius, the initial water-wet surface ratio, the relative adsorption thickness, and the surface coverage) on: (1) the flow enhancement; (2) the relative importance of all mechanisms; (3) the differences among organic pores/inorganic pores/micro-fractures; and (4) the overall contribution of asphaltenes. The effect of different adsorption patterns (characterized by the relative adsorption thickness and the surface coverage) is also discussed.