Tritium safety plays a crucial role in D-T fusion engineering. During normal operations, tritium(T) is typically dissolved with protium(H) or deuterium(D) in structural materials. However, there are still controversial issues related to the synergistic isotopic effects when considering T permeation through metals with H/D. In this work, a numerical model is built to describe the co-permeation behavior of multi-component hydrogen isotopes through metals in all rate-limited regimes. This model involves isotope exchange reactions in the gas phase, molecular dissolution, and atomic recombination at the gas-solid interface, as well as the diffusion process in the bulk. By simulating the mixed hydrogen gas permeation through various metals, different results are observed. In surface limited regime, the effective permeation flux of D is slightly enhanced by the presence of H due to isotopic effect. In diffusion-limited regime, the recombination of heteronuclear hydrogen molecules (HD) will deviate the equilibrium concentration of D on the upstream side from Sievert's Law, thereafter suppressing the D permeation flux on the downstream side.