The parallel broadcast channel with confidential messages (BCC) is investigated, where a source node transmits to two receivers (receivers 1 and 2) over multiple independent subchannels. The source node has common information for both receivers, and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The secrecy capacity region of the parallel BCC is established. It is shown that independent input distribution for each subchannel is optimal It is also shown that the secrecy capacity region of the parallel BCC can be larger than the sum of the secrecy capacity regions of the subchannels. The secrecy capacity region is further derived for the parallel BCC with degraded subchannels. Applications of these results to the fading BCC are also discussed.