As part of our multiwavelength campaign of GX 339-4 observations in 1996 we present our radio, X-ray, and gamma-ray observations made in July, when the source was in a hard state (= soft X-ray low state). The radio observations were made at the time when there was a possible radio jet. We show that the radio spectrum was flat and significantly variable, and that the radio spectral shape and amplitude at this time were not anomalous for this source. Daily light curves from our pointed observation July 9-23 using OSSE, from BATSE, and from the ASM on RXTE also show that there was no significant change in the X- and gamma-ray flux or hardness during the time the possible radio jet-like feature was seen. The higher energy portion of our pointed RXTE observation made July 26 can be equally well fit using simple power law times exponential (PLE) and Sunyaev-Titarchuk (ST) functions. An additional soft component is required, as well as a broad emission feature centered on 6.4 keV. This may be an iron line that is broadened by orbital Doppler motions and/or scattering off a hot medium. Its equivalent width is 600 eV. Our simplistic continuum fitting does not require an extra reflection component. Both a PLE and a ST model also fit our OSSE spectrum on its own. Although the observations are not quite simultaneous, combining the RXTE and CGRO spectra we find that the PLE model easily fits the joint spectrum. However, the ST model drops off too rapidly with increasing energies to give an acceptable joint fit.