The double pulsar J0737-3039 is the only known system in which the relativistic wind emitted by a radio pulsar demonstrably interacts with the magnetosphere of another one. We report radio interferometric observations of the J0737-3039 system with the VLA at three wavelengths, with each observation spanning a full binary orbit. We detect J0737-3039 at 1.6 and 4.8 GHz, derive a spectral index of -2.3 +/- 0.2, and place an upper limit on its flux density at 8.4 GHz. Orbital modulation is detected in the 1.6 GHz data with a significance of ~2 sigma. Both orbital phase-resolved and phase-averaged measurements at 1.6 GHz are consistent with the entire flux density arising from the pulsed emission of the two pulsars. Contrary to prior results, we find no evidence for unpulsed emission, and limit it to less than 0.5 mJy (5 sigma).
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