Interface specific second-harmonic (SH) and sum-frequency microscopes have been developed recently. In these microscopes, the two-dimensional intensity distribution of the nonlinear signal is used to create an image of the interface structure. In the intensity measurements, however, the phases of the nonlinear signals become obscured. The phases provide information on the absolute molecular orientation, which is not accessible in a corresponding linear optical experiment. Here we describe two homodyne techniques for the quantitative measurement of the absolute phases and their two-dimensional distribution. The data can be transformed into the polar molecular orientation field of an interface. As a model example, a Langmuir monolayer of organic molecules, 2-docosylamino-5-nitropyridine, is investigated. The SH and laser light are off resonance with the molecular dipole oscillators. In this case, the electromagnetic theory predicts a signal phase of 90° relative to the laser light. Intensity and homodyne images are taken. Dendritic features are observed in the monolayers. Any local feature which is clearly resolved in the images we consider as an individual sample whose local symmetry and polar order we determine. For the description of the features, it is important to introduce local sample coordinates. As we have shown recently, the point group of the local objects and the axial orientation of their molecules (orientation with an uncertainty of 180°) can be determined from a series of intensity images taken with different polarizer orientations. We may then fix a sample coordinate system at any local feature. One coordinate axis may correspond to the preferential molecular orientation of the feature. Since the absolute orientation of the molecules is not known at this state of the investigations, we may assume an arbitrary polar sign of this coordinate axis as a first hypothesis. If this sign agrees with the real sign of the molecular dipoles, we expect a phase of the SH signal of +90°. Since the inversion of a dipole's absolute orientation corresponds with a phase shift of 180° in the SH signal, we expect a phase of -90° if the real dipole orientation is opposite to the local coordinate axis. In the homodyne experiments, the intensity image of the interface is then coherently mixed with a spatially homogeneous SH signal from a reference sample. From the local homodyne intensities and the known phase of the reference signal, the local features' signal phase is calculated. The results (+90°, -90°) agree with the theory. Thus we can determine the absolute orientation of any local feature. In experiments, carried out near or in resonance, additional phases contribute to the SH signal. We show that the absolute dipole orientation can also be measured in these cases without ambiguity.