The non-luminous surroundings of atmospheric pressure plasma jets contain still substantial electron density which can be of practical importance, when e.g. reactant or precursor is introduced into this zone. Low signal-to-noise ratio makes the Stark broadening technique unsuitable there, and so we employed the microwave interferometry to determine the electron density during the plasma synthesis of graphene. The relatively long wavelength, tight geometry and the presence of overcritical plasma filament necessitated the use of a numerical solution of the Maxwell equations. Besides laying the groundwork of the method, the paper also discusses the importance of plasma density profile in the active filament and its surroundings. The results show that in radial distance ten times higher than a visually apparent plasma diameter, the plasma density was still around 1016-1017 m-3.