We introduce new polar coding schemes for independent non-identically distributed parallel binary discrete memoryless channels. The first scheme is developed for the case where underlying channels are time invariant (the case of a deterministic channel parameters), while the other schemes deal with a scenario where underlying channels change based on a distribution (the case of random channel parameters). For the former case, we also discuss the importance of the usage of an interleaver Q to enhance system reliability, and for the latter case, we model the channel behavior of binary erasure channels. It is shown that the proposed polar coding schemes achieve a symmetric capacity.