If you cannot agree in a divorce agreement or hearing, the court must decide. A rented home's lease can be transferred to one spouse regardless of who originally signed. The sole criterion is which spouse needs it more, considering children and the spouses' health and work circumstances. The departing spouse remains liable for rent only until the next termination date if the other fails to pay.
Even if only one spouse owns the home, a court may grant the other a residence right for a period. This is often done where that spouse has care of the children and they should remain in their familiar environment.
In short: If you cannot agree, a court may allocate the home to the spouse who needs it more. It does not matter who signed the lease or whether one spouse solely owns it.