I strongly recommend against.
You are from CA. So your debt means your husband's debt as well (community property). So it does not matter where you put it.
I am not sure how many credit cards both of you have in total. Based on your plan, you will effectively take 4 cards out of commission. Of course, you can continue to use it. You are simply not taking advantage of the BT offer.
Also - it is easier to pay off a single large balance than 4 separate balance. Beside, BT is designed for debt consolidation. In your case, you are not consolidating anything.
Both of you will take a hit on credit due to the balance. Since credit lines are available, I don't see why 2 people have to take the hit altogether.
If I were you, a single BT to Chase.