In this paper, the structured concatenated coding of protograph LDPC codes and markers for insertion and deletion channels are proposed, where the joint detector/decoder can deal with the differences in estimation accuracy of these errors. Conventional concatenated coding of LDPC codes and markers does not address the differences. The proposed approach with optimized protographs can exploit those differences and thus improve the performance of the joint detection/decoding. Iterative decoding thresholds and simulation results are provided to support the advantages of the proposed concatenated coding scheme.