  Common models for two-phase lipid bilayer membranes are based on an energy
that consists of an elastic term for each lipid phase and a line energy at
interfaces. Although such an energy controls only the length of interfaces, the
membrane surface is usually assumed to be at least $C^1$ across phase
boundaries. We consider the spontaneous curvature model for closed rotationally
symmetric two-phase membranes without excluding tangent discontinuities at
interfaces a priorily. We introduce a family of energies for smooth surfaces
and phase fields for the lipid phases and derive a sharp interface limit that
coincides with the $\Gamma$-limit on all reasonable membranes and extends the
classical model by assigning a bending energy also to tangent discontinuities.
The theoretical result is illustrated by numerical examples.
