The strength homogenization of cohesive-frictional solids influenced by the presence of two pressurized pore spaces of different characteristic sizes is addressed in this study. A two-scale homogenization model is developed based on limit analysis and the second-order method (SOM) in linear comparison composite theory, which resolves the nonlinear strength behavior through the use of linear comparison composites with optimally chosen properties. For the scale of the classical configuration of a porous solid, the formulation employs a compressible thermoelastic comparison composite to deliver closed-form expressions of strength criteria. Comparisons with numerical results reveal that the proposed homogenization estimates for drained conditions are adequate except for high triaxialities in the mean compressive strength regime. At the macroscopic scale of the double-porosity material, the SOM results are in agreement with strength criteria predicted by alternative micromechanics solutions for materials with purely cohesive solid matrices and drained conditions. The model predictions for the cohesive-frictional case show that drained strength development in granularlike composites is affected by the partitioning of porosity between micro- and macropores. In contrast, the drained strength is virtually equivalent for single- and double-porosity materials with matrix-inclusion morphologies. Finally, the second-order linear comparison composite approach confirms the applicability of an effective stress concept, previously proposed in the literature of homogenization of cohesive-frictional porous solids, for double-porosity materials subjected to similar pressures in the two pore spaces. For dissimilar pore pressures, the model analytically resolves the complex interplays of microstructure, solid properties, and volume fractions of phases, which cannot be recapitulated by the effective stress concept.