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Under the influence of the nonlinear fluid-solid coupling, hydraulic fracture exhibits various propagation modes (such as toughness- or viscosity-dominated), which stem from the competition between the solid deformation and fluid flow. Based on the homogeneous assumption, the basic theoretical analysis has divided toughness and viscosity scales in the tip region. However, regarding more realistic and complex geological conditions, like layered heterogeneity, knowledge of fluid-driven fracture propagation is still unclear. This work establishes a theoretical model and solving approach to reveal the multiscale asymptotic behavior during hydraulic fracture passing through the heterogeneous interface (i.e., discontinuous elastic properties). The influence of material discontinuity, regarded as the remote force, in the near-tip, intermediate, and far-field scales is analyzed by the asymptotic analysis and validated by the …