First-principles calculations offer a useful complement to experimental approaches for characterizing hydrogen permeance through dense metal membranes. A challenge in applying these methods to disordered alloys is to make quantitative predictions for the net solubility and diffusivity of interstitial H based on the spatially local information that can be obtained from first-principles calculations. In this study we used a combination of Density Functional Theory calculations and a cluster expansion method to describe interstitial H in alloys of composition Pd96M4 where M included Ag, Au, Cu, Ni, and Pt. We also applied these methods to alloys of composition Pd70Cu30 and Pd70Cu26M4 where M = Ag, Au, Ni and Pt. The cluster expansion approach highlights the shortcomings of simple lattice models that have been used in the past to study similar binary systems. We use Sieverts' law to calculate H solubility and a Kinetic Monte Carlo (KMC) scheme to find the diffusion of H in PdAg, PdAu, PdCu, PdNi, PdPt, PdCuAg, PdCuAu, PdCuNi, and PdCuPt alloys at a temperature range of 400 ≤ T ≤ 1200 K. From these results we are able to predict the permeability of hydrogen through thick membranes made from these Pd-based binary alloys and PdCu-based ternary alloys.