Because of the coupling between local lipid composition and the thickness of the membrane, microphase separation in two-component lipid membranes can take place; such effects may underlie the formation of equilibrium nanoscale rafts. Using a kinetic description, this phenomenon is analytically and numerically investigated. The phase diagram is constructed through the stability analysis for linearized kinetic equations, and conditions for microphase separation are discussed. Simulations of the full kinetic model reveal the development of equilibrium membrane nanostructures with various morphologies from the initial uniform state.