Macrophages in the lung detect and respond to influenza A virus (IAV), determining the nature of the immune response. Using terminal depth 5’-RNA sequencing (CAGE) we quantified transcriptional activity of both host and pathogen over a 24-hour timecourse of IAV infection in primary human monocyte-derived macrophages (MDM). This method allowed us to observe heterogenous host sequences incorporated into IAV mRNA, “snatched” 5’ RNA caps, and corresponding RNA sequences from host RNAs. In order to determine whether cap-snatching is random or exhibits a bias , we systematically compared host sequences incorporated into viral mRNA (“snatched”) against a complete survey of all background host RNA in the same cells, at the same time. Using a computational strategy designed to eliminate sources of bias due to read length, sequencing depth, multi-mapping, we were able to quantify over-representation of host RNA features among the sequences that were snatched by IAV. We demonstrate biased snatching of numerous host RNAs, particularly snRNAs, and avoidance of host transcripts encoding host ribosomal proteins, which are required by IAV for replication. We then used a systems approach to describe the transcriptional landscape of the host response to IAV, observing many new features, including a failure of IAV-treated MDMs to induce feedback inhibitors of inflammation, seen in response to other treatments.