My own assumption was that the two races interact freely in social, political, and economic matters: shopping at the same farmer's markets; attending the same zoning meetings; and, of course, drinking at the same pub. But I also inferred "minding their own affairs in their own ways" to mean that they maintain their own distinct subcultures in more private matters. I imagined there might be separate hobbit and human farmers' associations, for instance - which probably collaborate on matters of mutual interest, but remain distinct and handle a lot of their business on their own. And I suspect there wouldn't be a tailor or a barbershop which serves both hobbit and human clientèle in the same way as the Prancing Pony. I expected they would probably worship at different mosques/synagogues/churches/temples/shrines, and probably also have mostly segregated ceremonies for births (and birth days), Bar Mitzvahs, marriages, and funerals. Not strict demarcations, mind you - I wouldn't think a human at a hobbit wedding or funeral (or vice versa) would be a shocking, unthinkable occurrence, but I imagined it would be cause for more than a little gossip (not mean-spirited gossip, but something along the lines of, "Well, that's not something you see every day, is it?").
You're right that it was probably too hasty of me to run with these assumptions, and Mike's counter-proposal makes sense in light of the facts. I still my own interpretation is plausible, and still leaves room for prominent figures like the town innkeeper having knowledge of the townsfolk which transcends the species divide.