  In this paper we introduce a mesoscale continuum model for membranes made of
two different types of amphiphilic lipids. The model extends work by Peletier
and the second author [Arch. Ration. Mech. Anal. 193, 2009] for the one-phase
case. We present a mathematical analysis of the asymptotic reduction to the
macroscale when a key length parameter becomes arbitrarily small. We identify
two main contributions in the energy: one that can be connected to bending of
the overall structure and a second that describes the cost of the internal
phase separations. We prove the $\Gamma$-convergence towards a perimeter
functional for the phase separation energy and construct, in two dimensions,
recovery sequences for the convergence of the full energy towards a 2D
reduction of the J\"ulicher-Lipowsky bending energy with a line tension
contribution for phase separated hypersurfaces.
