You should communicate with your spouse about the situation, so that there are no surprises, no accusations that you mishandled marital assets or his separate property, and no other complications arising from the manner in which you decide to proceed. Have you already filed for divorce? If so, bring a motion on the issue in the divorce court.
At least on the surface, it sounds like it would be a good idea to recover your separate property. Presumably, given that he leased the unit, your spouse knows about the default and its imminent consequences.
How much time do you have before they're going to repossess the storage unit and sell the contents?

