Nanosheet-based membranes have shown enormous potential for energy-efficient molecular transport and separation applications, but designing these membranes for specific separations remains a great challenge due to the lack of good understanding of fluid transport mechanisms in complex nanochannels. We synthesized reduced MXene/graphene hetero-channel membranes with sub-1-nm pores for experimental measurements and theoretical modeling of their structures and fluid transport rates. Our experiments showed that upon complete rejection of salt and organic dyes, these membranes with subnanometer channels exhibit remarkably high solvent fluxes, and their solvent transport behavior is very different from their homo-structured counterparts. We proposed a subcontinuum flow model that enables accurate prediction of solvent flux in sub-1-nm slit-pore membranes by building a direct relationship between the solvent molecule-channel wall interaction and flux from the confined physical properties of a liquid and the structural parameters of the membranes. This work provides a basis for the rational design of nanosheet-based membranes for advanced separation and emerging nanofluidics.