It is now well established that in the gel-fluid phase coexisting region of bilayers made of two mixed phospholipids, one of the phases is microdispersed in the other. On the basis of data obtained with fluorescence recovery after photobleaching for 1,2-dimyristoyl-sn-glycero-(3)-phosphocholine/1,2-distearoyl-sn-glycero-(3)-phosphocholine (DMPC/DSPC) mixtures, the linear dimension of the rigid domains for small rigid phase fractions was predicted to be 2-3 mum (Coelho, F. P.; Vat, W. L. C.; Melo, E. Biophys. J. 1997, 72, 1501) and therefore, much smaller than the domains obtained with monolayers with identical composition. Recent 'nanoscopic" observations confirmed that this was a reasonable estimate. In this work, we explain this difference in dimension, ascribing it to the interaction of the polarized surface of the two opposing domains pertaining to the two bilayer leaflets. It is shown that the geometry of the rigid structures formed is strongly dependent on the bilayer core dielectric permittivity. It is also found that in bilayers a circular to elliptic shape transition, similar to the one predicted for monolayers, is to be expected.