Conventional hybrid RF and optical wireless communication systems make use of parallel Free Space Optical (FSO) and Radio Frequency (RF) channels to achieve higher reliability than individual channels. True hybridization can be accomplished when both channels collaboratively compensate the shortcomings of each other and thereby improve the performance of the system as a whole. In this paper, we propose a novel coding paradigm called "Hybrid Channel Coding" that not only optimally achieves the capacity of the combined FSO and RF channels but also can potentially provide carrier grade reliability (99.999%) for hybrid FSO/RF systems. The proposed mechanism uses non-uniform and rate-compatible LDPC codes to achieve the desired reliability and capacity limits. We propose a design methodology for constructing these Hybrid Channel Codes. Using analysis and simulation, we show that by using Hybrid Channel Codes, we can obtain significantly better availability results in terms of the required link margin while the average throughput obtained is more than 33% better than the currently existing systems. Also by avoiding data duplication, we preserve to a great extent the crucial security benefits of FSO communications. Simulations also show that Hybrid Channel Codes can achieve more than two orders of magnitude improvement in bit error rate compared to present systems.