Genes and human languages are discrete combinatorial systems (DCSs), in which the basic building blocks are finite sets of elementary units: nucleotides or codons in a DNA sequence, and letters or words in a language. Different combinations of these finite units give rise to potentially infinite numbers of genes or sentences. This type of DCSs can be represented as an alphabetic bipartite network (ABN) where there are two kinds of nodes, one type represents the elementary units while the other type represents their combinations. Here, we extend and generalize recent analytical findings for ABNs derived in [Peruani et al., Europhys. Lett. 79, 28001 (2007)] and empirically investigate two real world systems in terms of ABNs, the codon gene and the phoneme-language network. The one-mode projections onto the elementary basic units are also studied theoretically as well as in real world ABNs. We propose the use of ABNs as a means for inferring the mechanisms underlying the growth of real world DCSs.