A small pit, depression, or invagination, such as any of the minute pits or incuppings of the host cell membrane formed during pinocytosis, that communicates with the outside of a host cell and extends inward, indenting the host cytoplasm and the host cell membrane. Such caveolae may be pinched off to form free vesicles within the host cytoplasm. The host is defined as the larger of the organisms involved in a symbiotic interaction.