The objective of this paper is to model the synergistic bond-degradation mechanisms that may occur at the interface between a fiber-reinforced polymer (FRP) that is adhesively bonded to a substrate and subjected to elevated temperature and humidity. For this purpose, a two-dimensional cohesive-layer constitutive model with a prescribed traction-separation law is constructed from fundamental principles of continuum mechanics and thermodynamics, taking into account strain-dependent, non-Fickian hygrothermal effects as well as diffusion-induced degradation in the cohesive layer. In the interest of solution tractability, a simplified approach is employed where the rate-dependent behavior in the cohesive layer is implemented through the characterization of rate dependence of the maximum stresses and maximum strains in the cohesive layer, rather than through the use of convolution integrals in the free-energy definition. The remainder of the polymeric adhesive outside the cohesive layer is modeled as a nonlinear viscoelastic continuum with time-dependent constitutive behavior. The influence of temperature and moisture concentration on the work-of-separation and on crack growth is derived from first principles. The model is implemented in a test-bed finite element code. Results predicted by the computational model are benchmarked through comparison to experimental data from mixed-mode fracture experiments performed using a moving wedge test.