You might be able to get a court order and serve it on the bank, so they cannot allow him or her access to the box without you or your attorney present. It would also be prudent to subpoena the bank for any records they have on your wife/husband. You may find that he or she has other accounts that you don't know about. If you're in a community property State, the contents of the box (whatever they are) may be deemed to be communal property and subject to the division of marital assets, especially if the box is paid through by a joint (communal) account.
There are exceptions to this, however. If the box is listed solely in their name (they are the only one listed that can sign to get into the box), you may have a more difficult time proving it to be a marital asset, even in a community property State.