In this paper, we develop a dual-porosity dual-permeability model for binary gas migration to explore the permeability evolution in the matrix and fracture in the process of a gas-water two-phase flow during CO₂-enhanced coalbed methane (CO₂-ECBM) recovery in coal reservoirs. This mechanistic model accommodates the effects of elastic deformation caused by the effective stress change in the matrix and fracture, the swelling/shrinkage deformation of the matrix caused by adsorption/desorption, the convection and diffusion of gas, and the discharge of water. Specifically, the time-dependent matrix swelling, from initially completely reducing the fracture aperture to finally affecting the coal bulk volume, is considered by the invaded volume fraction involving binary gas intrusion. The model is validated through laboratory data and applied to examine the permeability evolution of CO₂-ECBM recovery for 10 000 days. Furthermore, we analyze the sensitivity of some selected initial parameters to capture the key factors affecting CO₂-ECBM recovery. Our modeling results show that the permeability evolution can be divided into two stages during the process, where stage I is dominated by effective stress and stage II is dominated by adsorption/desorption. Increasing the injection pressure or initial permeability advances the start of stage II. The decrease in initial water saturation causes the permeability to change more drastically and the time of stage II to appear earlier until a time long enough, after which little effect is seen on the permeability results.