There is a news story of interest from a few weeks ago in the NY Times:
It discusses the concept and some of the research on how animals and their microbiomes could in some cases play a role in shaping the human immune system and human microbiomes. The article also discusses some built environment studies such as the Wildlife of Your Homes project and others. The article does not take quite enough of a skeptical point of view for me but it does present some caveats (e.g., that pets can also be carriers of pathogens). But it is worth a look.