"I have special ties to Wisconsin and Milwaukee in particular. Both mine and my wife's family are spread throughout the greater Milwaukee area." I was unsure about, "...mine and my wife's family" I mean, I didn't think it should be, "my and my wife's family"? But not sure if what I have is correct either.
I would say: Both my wife's family and mine are spread.... This, in obeisance to the order of operation for presenting different people in a list: Third person, second person, first person, in that order. It's not just politesse. Notice how the mine feels more grounded this way? Now, if this were dialogue and you were presenting someone whose grammar isn't as fastidious as that, at least in the U.S., the convention is to turn I into me when the first person is presented first in a list, even when it's intended to be a possessive, which is confusing as all get-out, but when I say it to myself that's what feels natural for that particular kind of speaker. Both me and my wife's family are spread....
I agree with Wrey. When I first see "mine," I'm not sure what it's referring to. Having "my wife's family" first makes it clear you're referring to your own family.
"I have special ties to Wisconsin, Milwaukee in particular. Both my family, my wife's family, are spread throughout the greater Milwaukee area. Together, we, I suppose, are akin to a spawn of Satan [frogs] scattered over the American Mid-West, over the Great Lakes region. Our twelve children, our one hundred and twenty four grandchildren dominate society at each and every level in every village, upon every ranch. One day I will be president."
I like the way Wrey's phrased it, but if you're looking to keep yours, it'd be "my and my wife's". The way I learned, you remove the list sort of part (brain's fried atm, can't think of what term I need) and see if it still makes sense. "Mine family" would be wrong, so "mine and my wife's family" is wrong.