The variability of the interference pattern of a narrow-band sound signal in a shallow water waveguide in the horizontal plane in the presence of horizontal stratification, in particular due to linear internal waves, is studied. It is shown that lines of constant phase (a phase front) and lines of constant amplitude/envelope (an amplitude front) for each waveguide mode may have different directions in the spatial vicinity of the point of reception. The angle between them depends on the waveguide's parameters, the mode number, and the sound frequency. Theoretical estimates and data processing methodology for obtaining these angles from experimental data recorded by a horizontal line array are proposed. The behavior of the angles, which are obtained for two episodes from the Shallow Water 2006 (SW06) experiment, show agreement with the theory presented.