Since I don't know the exact story, it's hard to give a precise example. But perhaps in the story, the wife has a business connection. The hubby, being part of her network through marriage, uses that connection to get a deal where instead of paying money directly, he exchanges services or resources based on that connection, which could be seen as 'paying with wife'.
Well, if the 'hubby pays with wife story' is about using intangible aspects of the wife. For example, the wife is very well - known in a small town for her baking skills. The hubby enters a baking competition on behalf of her (since he has learned from her) and wins a prize that can be used to pay off a debt. So he's using her skills and reputation, in a sense, to 'pay'.
In the 'hubby pays with wife story', one example could be that the wife is an artist. She has a lot of her artworks stored. The hubby, who is an art dealer, uses her artworks to trade with another collector for something valuable. This valuable item is then used to pay for something they needed, like a new car. Here, he is using his wife's assets (her artworks) to make the payment.