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The interfaces between graphene and graphane play an important role in developing graphene-graphane-based electronic devices. We identify three most common types of graphane-graphene interface, and perform atomistic simulations to determine three key parameters that characterize the interface structural properties: mismatch strain, tilt angle, and interfacial stress. Further through atomistic simulations, we find that the composite sheets can develop complex morphologies, such as ripples, warps and wedges. These morphologies can be accurately reproduced by our finite-element modeling with interfacial properties explicitly included. We further show that mismatch in the lattice parameters between graphene and graphane is the dominant factor that causes the complex morphologies. Our work provides a quantitative framework for analyzing and designing graphene-graphane composite sheet architectures, and further for exploring their electronic properties. [ABSTRACT FROM AUTHOR]