Housing Solution in a Divorce?

[Militant Agnostic]

My husband and I agreed to divorce after 12 years of marriage and 4 kids. We agreed to split the kids 50/50. Neither of us can afford our house without both of our incomes and finding 2 houses that have 4 bedrooms that are affordable in our small town seems impossible. So I came up with a possible solution and was wondering what the legal ramifications would be.

What if my future ex husband co-rent an apartment together and when it is my week without the kids, I would stay there and he could stay at the house and visa versa. I know this might sound strange and I wouldn't want it to be permanent but until we can both save up enough money to buy a decent house on our own, we could split the mortgage, utility payments and the rent.

My husband and I have a unique relationship and I think he would agree to it. I could find a 2 bedroom and we would be like roommates that never see each other.

Thoughts?
We aren't divorcing because we hate each other. We just got married for the wrong reasons and decided that the kids are old enough now for us to part ways.

I also think we could afford an apartment a lot easier than 2 separate houses. It wouldn't have to be anything spectacular if it is just him and I living there.
I got married in a courthouse in front of a judge, not a god.