My husband and I decided to separate for awhile so he co-signed on a lease for me and our kids.

There are two different issues here:  The first is that under the lease, anyone who signs the lease is obligated under the lease for the rent and any damages.  If you were to break your lease or not pay the rent, he could and would be held liable in addition to you.  If they had to evict you, they would include his name in the eviction. The second is in regards to the divorce matter.  In the property and debt allocation portion of the divorce, you could be found liable 100% for the rent and if he was sued for any unpaid rent, you would be liable to pay it and/or pay him back any money he has to pay to satisfy the judgment.  This is only if you two don't come to an agreement as to how the debts and property will be divided up and it is entered into a final judgment.