Consider a set of sensors that wish to consent on the message broadcasted by a multi-antenna transmitter in the presence of white-noise jamming. The jammer's interference introduces correlation across receivers and destroys the decomposable form of the maximum-likelihood decoder, thus preventing direct application of known distributed detection algorithms. This paper develops distributed detectors that circumvent this problem. Treating the jammer signal as deterministic, we develop two distributed estimation-decoding algorithms. The first algorithm relies on the generalized likelihood ratio test, whereas the second algorithm relies on semi-definite relaxation techniques and is suitable for large alphabet sizes. Both algorithms feature: (i) distributed implementation requiring only single-hop communications; (ii) no constraints on the network topology so long as it is connected; and (iii) performance close to the optimum centralized detector in the presence of severe jamming.