We investigate a K-user parallel packet-erasure broadcast channel. There is an ongoing effort to harness millimeter-wave bands, which are known to be unstable having high outage probabilities, by combining them with stable legacy bands. Motivated by this effort, we consider a heterogeneous scenario in which the parallel subchannels are categorized into two classes having different outage probabilities. For the two-user case, we characterize the sum capacity by developing an explicit achievable scheme and deriving a matching upper bound. In contrast to suboptimal schemes that apply coding on a per-subchannel basis only, our scheme applies coding across subchannels to exploit coding opportunities that arise from asymmetric outage probabilities more efficiently, thereby achieving optimality. By extending our scheme systematically to be applicable for the K-user case, we show that it can provide significant gains over existing schemes. Compared to the K-user scheme currently employed in practice, which allocates chunks of subchannels to users exclusively, we demonstrate the performance improvement attainable by our scheme to be substantial, as the multiplicative gain scales with K. Moreover, we find that our scheme outperforms a per-subchannel extension of state-of-the-art K-user schemes by large margins, further reducing the optimality gap. Our results suggest a potential coding scheme that can be employed in future wireless systems to meet ever-growing mobile data demands.