Observations have been made of systematic patterns in VLF hiss, which can be interpreted as a standing wave pattern formed by reflection in the lower ionosphere. Multicomponent VLF electric and magnetic field experiments were flown on three sounding rockets (Nike-Tomahawk 18.203-205) from Siple station, Antarctica during December 1980 to January 1981. One feature of the natural emissions was observed in a very similar form during each flight. A band of hiss, typically from 1.5 to 3 kHz, was seen on the upleg to form a series of closely spaced stripes with whistler-like dispersion. These first appeared at an altitude of 90--95 km and extended for as much as 40 km in altitude. On the downleg the stripes were observed at the same altitude with the pattern reversed in time. No such patterns were observed by the VLF receivers operating at the same time on the ground at Siple or at its conjugate point. It is suggested that the patterns are interference effects due to downcoming waves reflecting from a layer in the E region and forming a standing wave pattern. The observed stripes are then due to the rocket traversing the standing wave pattern in opposite directions on upleg and downleg. If this interpretation is correct, the fringe spacing should be related to the wavelength and permits a calculation of the refractive index. In one example we calculate n=43.7 in good agreement with two independent determinations of the refractive index.