<p>A novel mathematical model has been formulated to explore the dynamics of two distinct infectious diseases, HBV and HIV, incorporating standard incidence rates. The model integrates vertical transmission mechanisms for both diseases and considers imperfect vaccination for HBV. To capture the inherent memory effects associated with these diseases, fractional-order derivatives are employed. The existence, uniqueness, and stability of the model are rigorously established through advanced fixed-point theory and stability analysis. Moreover, the global asymptotic stability of the infection-free equilibria is also assessed. For numerical approximation, the Nonstandard Finite Difference (NSFD) method is applied, with a thorough investigation of the impact of various denominator functions on the stability and behavior of the numerical solutions. It is observed that the choice of denominator function can significantly influence the trajectory of the disease dynamics. A comparison of the developed NSFD for the model and ODE-45 solver is also presented for different fractional orders. Simulations are presented to illustrate the effect of fractional-order derivatives on the evolution of the model’s compartments. The simulation graphs about the impact of vaccination tell that one can reduce the burden of the disease by increasing the vaccination rate or increasing the efficacy of the vaccine. Some simulations for the effects of vertical transmissions are also presented.</p>