Vital biological processes, such as trafficking, sensing, and motility, are facilitated by cellular lipid membranes, which interact mechanically with surrounding fluids. Such lipid membranes are only a few nanometers thick and composed of a liquid crystalline structure known as the lipid bilayer. Here, we introduce an active, noncontact, two-point microrheology technique combining multiple optical tweezers probes with planar freestanding lipid bilayers accessible on both sides. We use the method to quantify both fluid slip close to the bilayer surface and transmission of fluid flow across the structure, and we use numerical simulations to determine the monolayer viscosity and the intermonolayer friction. We find that these physical properties are highly dependent on the molecular structure of the lipids in the bilayer. We compare ordered-phase with liquid disordered-phase lipid bilayers, and we find the ordered-phase bilayers to be 10 to 100 times more viscous but with 100 times less intermonolayer friction. When a local shear is applied by the optical tweezers, the ultralow intermonolayer friction results in full slip of the two leaflets relative to each other and as a consequence, no shear transmission across the membrane. Our study sheds light on the physical principles governing the transfer of shear forces by and through lipid membranes, which underpin cell behavior and homeostasis.