In recent work [Vaz, W. L. C., Melo, E. C. C., & Thompson, T. E. (1989) Biophys. J. 56, 869-876] we have shown that translational diffusion studies using fluorescence recovery after photobleaching (FRAP) provide information concerning domain structures and fluid-phase connectivity in lipid bilayers in which solid and fluid phases coexist. In the present paper, translational diffusion of the fluid-phase-soluble, solid-phase-insoluble fluorescent lipid derivative N-(7-nitrobenzoxa-2,3-diazol-4-yl)dilauroyl-phosphatidylethanolamine and the fluid-phase connectivity are examined in lipid bilayers prepared from binary mixtures of 1-docosanoyl-2-dodecanoylphosphatidylcholine (C22:0C12:0PC) and 1,2-diheptadecanoylphosphatidylcholine (di-C17:0PC) by using FRAP. The phosphatidylcholine mixture used provides a eutectic system with a eutectic point at a composition of about 0.4 mole fraction of di-C17:0PC and a temperature of about 37-degrees-C [Sisk, R. B., Wang, Z. Q., Lin, H. N., & Huang, C. H. (1990) Biophys. J. 58, 777-783]. Two regions in temperature and composition, respectively below and above 0.4 mole fraction of di-C17:0PC, where fluid and solid phases coexist in the same lipid bilayer, are available for examination of fluid-phase connectivity. In mixtures containing < 0.4 mole fraction of di-C17:0PC the fluid phase coexists with a mixed interdigitated L(c) gel phase composed mostly of C22:0C12:0PC, whereas in mixtures containing > 0.4 mole fraction of di-C17:0PC the fluid phase coexists with a P-beta' gel phase mostly composed of di-C17:0PC. When the solid phase is a P-beta' gel phase, the temperature of fluid-phase connectivity for the mixtures lies close to the fluidus, which means that a small (almost-equal-to 20%) mass fraction of solid phase can divide the large bulk of the bilayer that is fluid into nonconnected domains. A reticular structure is inferred for the continuous P-beta' gel phase domain in this case. When the solid phase is a mixed interdigitated L(c) gel phase, the temperature of fluid-phase connectivity for the mixtures lies almost at the solidus, which means that a very small (less-than-or-equal-to 10%) mass fraction of fluid phase forms a continuous domain even when the large bulk of the bilayer is in a solid phase. This implies a reticular structure for the fluid phase and an insular structure for the L(c) gel phase domains in the system. We try to understand the result in terms of continuum percolation models and discuss possible domain structures in these lipid bilayers.