Significance Influenza A viruses (IAV) can exchange genetic material in coinfected cells in a process termed reassortment. The last three IAV pandemic strains arose from reassortment events involving human and nonhuman IAVs. Because introduction of the hemagglutinin (HA) gene from a nonhuman virus is required for a pandemic, we addressed the compatibility of human and avian IAV. We show that sequence differences between human and avian HA genes limit the potential for reassortment. However, human IAV still incorporated heterologous HA genes at a low level in coinfected animals. This observed low level of incorporation could become significant if reassortant viruses had a fitness advantage within the host, such as resistance to preexisting immunity, and highlights the continued need for IAV surveillance.