Motivated by recent efforts to harness millimeter-wave (mmWave) bands, known to have high outage probabilities, we explore a K-user parallel packet-erasure broadcast channel that consists of orthogonal subchannels prone to packet-erasures. Our main result is two-fold. First, in the homogeneous channel where all subchannels have the same erasure probability, we show that the separation principle holds, i.e., coding across subchannels provides no gain. Second, in the heterogeneous channel where the subchannels have different erasure probabilities, we devise a scheme that employs coding across subchannels and show that the principle fails to hold, i.e., coding across subchannels provides a gain. Inspired by this finding, we demonstrate our scheme to be effective in harnessing the mmWave bands. Compared to the current approach in the 4G systems which allocates subchannels to users exclusively, we show that our scheme offers a huge gain. We find the gain to be significant in scenarios where the erasure probabilities are largely different, and importantly to increase with the growth of K. Our result calls for joint coding schemes in future wireless systems to meet growing mobile data demands.