Another poster said it but I'll echo it again - while it's great to share biking with your wife and kids, it's also nice to give your wife some alone time. My wife is not completely into the biking thing. Our kids are young - 3 and 1 - so when I take them out biking they are either in a bike trailer behind me or the 3 year old is on his little bike with training wheels and I push the 1 year old in the stroller, and my wife jogs with. If I'm pulling the trailer, she goes running on her own.
So we all get good exercise in our own way. She's ridden my bike a few times and doesn't mind it, just doesn't have a strong desire to do it, she prefers running. I think maybe when the kids are a little older and both on bikes, street safe, it might be a little more convincing to her to be on her bike (she has a mountain bike from her teenage years, fixed up in usable shape).