The innate immune response provides a first line of defense against pathogens by targeting generic differential features that are present in foreign organisms but not in the host. These innate responses generate selection forces acting both in pathogens and hosts that further determine their co-evolution. Here we analyze the nucleic acid sequence fingerprints of these selection forces acting in parallel on both host innate immune genes and ssRNA viral genomes. We do this by identifying dinucleotide biases in the coding regions of innate immune response genes in plasmacytoid dendritic cells, and then use this signal to identify other significant host innate immune genes. The persistence of these biases in the orthologous groups of genes in humans and chickens is also examined. We then compare the significant motifs in highly expressed genes of the innate immune system to those in ssRNA viruses and study the evolution of these motifs in the H1N1 influenza genome. We argue that the significant under-represented motif pattern of CpG in an AU context--which is found in both the ssRNA viruses and innate genes, and has decreased throughout the history of H1N1 influenza replication in humans--is immunostimulatory and has been selected against during the co-evolution of viruses and host innate immune genes. This shows how differences in host immune biology can drive the evolution of viruses that jump into species with different immune priorities than the original host.