Orientation of lipophilic dye molecules within a biological membrane can report on the molecular environment, i.e., the physical and chemical properties of the surrounding membrane. This fact, however, remains under-utilized, largely because of our limited quantitative knowledge of molecular orientational distributions and the fact that robust techniques allowing experimental observation of molecular orientations of dyes in biological membranes are only being developed. In order to begin filling this lack of knowledge and to develop appropriate tools, we have investigated the membrane orientational distribution of the 3-hydroxyflavone-based membrane dye F2N12S. Results of our single- and two-photon polarization microscopy observations of linear dichroism of F2N12S-labeled giant unilamellar vesicles are consistent with a Gaussian-like orientational distribution of the transition dipole moment of the dye, with a mean tilt angle of 53.2 +/- 0.1 degrees with respect to the bilayer normal and a standard deviation of 13.3 +/- 0.6 degrees. Independently, by combining quantum chemical calculations and molecular dynamics simulations, we obtained very similar values; a mean tilt angle of 48 +/- 4 degrees and a standard deviation of 13 +/- 2 degrees. The good agreement between the experimentally and computationally obtained values cross-validates both approaches and gives confidence to the results obtained. The results open a door to robust quantitative determinations of orientational distributions of fluorescent molecules (ranging from simple synthetic dyes to fluorescent proteins attached to membrane proteins) associated with lipid membranes. Such determinations enable rational development of a novel class of sensitive fluorescent optical probes, reporting on cellular events through changes in linear dichroism.