Owing to their unique hetero-deformation induced strengthening and strain hardening (HDI) effect, bimodal structure alloys can exhibit excellent strength–ductility synergy. However, the roles of the HDI mechanism remain incompletely understood. This study establishes a micromechanical model of the bimodal structure of pure Cu with 230 nm fine grains and 3 μm coarse grains as an example and estimates the HDI effects on the mechanical properties of Cu. This model is based on the Mori–Tanaka mean field method. The bimodal structure comprises a particulate inclusion phase of coarse grains (soft zone) and a hard matrix phase of fine grains (hard zone). Combining plastic strain gradient and dislocation theories, the HDI effect is proposed as a three-stage process of soft zone hardening, hard zone softening, and stress repartitioning, thereby providing quantitative assessments of the HDI effects on the overall mechanical behaviors of bimodal copper. Based on the experimental observations, the forward stress effect is considered to result from softening via the disentanglement and annihilation of entangled dislocations and from hardening caused by shear band formations. The model predictions favorably agree with the existing experimental data. The role of the forward stress effect in the mechanical response is apparently enhanced when the hard zone (230 nm grains) completely encloses the soft zone (3 μm grains). Moreover, increasing the volume fraction of the soft zone decreases the overall strength and reduces the ductility of Cu. At soft zone fractions of 25%–35%, the strength and ductility were optimally balanced with a tensile strength of 417–420 MPa and an elongation of 28.2%–29.8%. The ultimate tensile strength and elongation were 7% lower and 10-fold higher, respectively, than those of unimodal 230-nm-grained Cu and almost doubled and halved, respectively, from those of unimodal 3-μm-grained Cu.