||We propose a model that accounts for the budding behavior of domains in lipid bilayers, where each of the bilayer leaflets has a coupling between its local curvature and the local lipid composition. The compositional asymmetry between the two monolayers leads to an overall spontaneous curvature. The membrane free energy contains three contributions: the bending energy, the line tension, and a Landau free energy for a lateral phase separation. Within a mean-field treatment, we obtain various phase diagrams which contain fully budded, dimpled, and flat states. In particular, for some range of membrane parameters, the phase diagrams exhibit a tricritical behavior as well as a three-phase coexistence region. The global phase diagrams can be divided into three types and are analyzed in terms of the curvature-composition coupling parameter and domain size.