A phase-separating elastic system is studied to investigate the morphological dynamics in mixed lipid bilayers. 
The system can realize two kinds of interactions, elastic and trans-bilayer coupling. 
In the numerical simulations, even in simple situations with homogeneous and isotropic moduli, 
some characteristic intramembrane subdomain structures can be observed. 
The elastic interaction produces fine, distinctive morphology in the lipid membrane 
and the trans-bilayer coupling interaction regulates the symmetry of the two leaflets of the bilayer. 
On the basis of the numerical observation, some special states are formulated to simplify the system 
and to focus on the elastic interaction. 
Several mathematical properties of the resulting steady states are presented. 
In particular, it is proved that the elastic interaction stabilizes intramembrane subdomain structures 
by secondary bifurcations of the steady states.