In previous work, phenomenological equations for the poroelastic behavior of a double-porosity dual-permeability medium (i.e., low-permeability storage porosity and high-permeability transport porosity both present in the same three-dimensional (3-D) volume) were formulated, and the coefficients in these equations were identified. In the present work, models are given instead that allow all of these coefficients to be determined from the underlying constituents' properties. Two different models are provided for the six geomechanical constants in the isotropic theory. In one model the low-permeability storage porosity is assumed to be a mixture of two porous materials in nonwelded or partially welded contact, and the high-permeability joint porosity develops as a misfit porosity at the interface between the two partially welded constituents. In this model the joint phase is 100% fluid. In the other model the low-permeability storage porosity is modeled as a single uniform porous material, while the high-permeability joint porosity is modeled as a second distinct porous material in welded contact with the first. In this model the joint phase is a porous continuum possessing a skeletal framework representing the asperities and gouge material that are present in real joints. The complete set of formulas needed for forward modeling the geomechanical constants is obtained for both scenarios. Examples are evaluated with these formulas, and comparisons are made to previous results on double-porosity systems analysis.