Recently, the universality of a well-designed LDPC code ensemble has been recognized. Take the DVB standards for example. The structured LDPC codes originally developed for satellite communications have been reused in terrestrial and cable channels. To this end, a bit interleaver can be employed to adapt the profile of the given code to the variation of channel conditions. In this paper, we focus on the design of code-dependent bit interleavers for parallel non-uniform channels. Since the channel- dependence of a given code ensemble is dominated by the mutual information between the channel input and output, we propose to simplify the analysis about the decoding behavior by using a set of surrogate binary erasure channels (BEC). The approximation of the actual channel by the surrogate BEC is established on the equivalence of bitwise capacities, which represent the mutual information between the uniformly-distributed binary input and the likelihood ratios of the effective parallel AWGN channels. Moreover, the transition of the erasure probabilities is modeled by a linear difference equation around the decoding threshold SNR, from which we can derive a necessary condition on the convergence of decoding iterations and achieve a useful guideline for the configuration of the bit interleavers.