I am submissive to hubby. I am not less than hubby. Therefore, there is no contending for a role.
Here's how that works out in our household. I am the checkbook balancer, bill payer, best-deal-getter for insurances, phones and any other services we'll be spending money more than once, and taxes-deal-with-er. I get the car inspected, make sure yearly forms are filled out and returned in a timely way. I am the one he consults with if he wants to buy something relatively expensive, not because he needs my permission, but he needs to know if we have the money to afford the expense. If I spend more than $20 on something not-bill-related or not-household-purposed, I ask. ("Should we buy the Narnia series on DVD?" "Mind if I buy some new jammies?")
I'm also gifted in getting through to people we need to get through to, when it seems like nothing but message machines that never get anywhere. (He too is disabled, so can't do jury duty. Tried to respond to the summons online, which simply defaults to "there is no excuse. Come." So I had to find the right person he could talk to, so he wouldn't be arrested for not going. And my chair is broken, the company promised to fix it, but SNAFU-ed up the wazoo, but I talked to the right people to resolve that. It's an odd gift, but if I need to get something done when first-tier help desks simply say No, I can find the one who will say Yes.)
I also am the laundry-doer, the take-out-the-trash-er, Dessert Chef, and I'm the Chief Bottle Washer 70% of the time.
He is the 3-5 Star Master Chef and Griller. When the meals doesn't turn out good, it's only worth 3-stars, but, man! He can so cook. We had shrimp in a mushroom, scallions and tomatoes (both from our garden) on store-bought gnocchi last night. (He's made sweet-potato gnocchi, but sometimes it's just easier to use store-bought.) It was definitely 5-star all the way! He's also the frig and cabinet cleaner, and we share who gets stuck cleaning the stove and/or oven. And, if I take on a big project that is too big for me, he pitches in to help. (A rusty grill had to go in the trash. I thought it would fall apart enough that I could handle it. It didn't, so hubby stepped in to help. And the garden box for our tomatoes got a gash in the bottom, so he took over to replace it. Ever try to lift three tomato plants in the middle of summer -- soil included? lol)
The rest of the chores and household responsibilities were negotiated long ago, under the "if it bothers you, do something about it" clause. lol
Because of that, I didn't get the first half of what you wrote. (Even got a bit lost on the scripture, since I don't know where it's from, but that's on me. lol) There doesn't have to be strict male/female roles in the home. It's not really like men have to deal with bills and women have to cook. It's what works to the strength of the two in the marriage. And, if it can't be negotiated, and, if it can't be voted as consensus, then the husband gets the final vote.
Given the wife and husband are always submitting to God, (hey, and we really can't slough on that one, since the spouse has to rely on that submitting for it to work), the husband loves the wife like Christ loves his Church, and the woman submits and loves the husband, it's not an employer-employee relationship. It's a partnership, with God as the boss.