Infection with influenza A virus (IAV) infection is responsible for an estimated 500,000 deaths and up to 5 million cases of severe respiratory illness each year. In this study, we looked at human primary immune cells (macrophages) infected with IAV. Our method allows us to look at both the host and the virus in parallel. We used these data to explore a process known as “cap-snatching,” where IAV snatches a short nucleotide sequence from capped host RNA. This process was believed to be random. We demonstrate biased snatching of numerous host RNAs, including those associated with snRNA transcription, and avoidance of host transcripts encoding host ribosomal proteins, which are required by IAV for replication. We then describe the transcriptional landscape of the host response to IAV, observing new features, including a failure of IAV-treated MDMs to induce feedback inhibitors of inflammation, seen in response to other treatments.