In this paper, we introduce a deep learning-based decoder designed for concatenated coding schemes over a deletion/substitution channel. Specifically, we focus on serially concatenated codes, where the outer code is either a convolutional or a low-density parity-check (LDPC) code, and the inner code is a marker code. We utilize Bidirectional Gated Recurrent Units (BI-GRUs) as log-likelihood ratio (LLR) estimators and outer code decoders for estimating the message bits. Our results indicate that decoders powered by BI-GRUs perform comparably in terms of error rates with the MAP detection of the marker code. We also find that a single network can work well for a wide range of channel parameters. In addition, it is possible to use a single BI-GRU based network to estimate the message bits via one-shot decoding when the outer code is a convolutional code.