We use simulations to predict the stability and mechanical properties of two amphiphilic bilayer membranes. We carry out atomistic MD simulations and investigate whether it is possible to use an existing coarse-grained (CG) surfactant model to map the membrane properties. We find that certain membranes can be represented well by the CG model, whereas others cannot. Atomistic MD simulations of the erucate membrane yield a headgroup area per surfactant a0 of 0.26 nm2, an elastic modulus KA of 1.7 N/m, and a bending rigidity κ of 5 kBT. We find that the CG model, with the right choice for the size and potential well depth of the head, correctly reproduces a0, κ, as well as the fluctuation spectrum over the whole range of q values. Atomistic MD simulations of EHAC, on the other hand, suggest that this membrane is unstable. This is indicated by the fact that κ is of the order of kBT, which means that the interface is extremely flexible and diffuse, and KA is close to zero, which means that the surface tension is zero. We argue that the CG model can be used if the headgroups are uncharged, dipolar, or effectively dipolar due to headgroup charge screening induced by counterion condensation.