Never heard of a Moth 3 before. This must have been very early in its production and so named because of the 3 seats? "And Mother came too!", or perhaps your professional pilot. Very strange seating arrangements to my modern eyes. From the landing gear struts going right up to the wing root, a Puss Moth.
Presumably the Three comes from the de Havilland Gipsy III engine used in the early Puss Moths before the more usual Gipsy Major, both running inverted compared to the early Moths?
The prototype DH.80 Moth Three first flew from Stag Lane on 9 September 1929 but went into production in a much modified form as the DH.80A Puss Moth. The main change was to the design of the fuselage. The prototype had conventional wooden longerons but this was changed to welded steel tube based on knowledge gained from the DH60M Moth. John R