The two of you can AGREE to whatever you want. If you go through a legal separation, you do have the option of keeping your spouse on the insurance. However, if you divorce, by law, you are required to inform the insurance carrier of the divorce. Most insurance carriers will not cover ex-spouses. Please note, however, that upon filing for separation or divorce there are automatic temporary restraining orders. These orders require that you keep everything as is - no removal from insurances, no closing bank accounts and credit accounts - except as in the normal course of daily life (paying utilities, groceries, etc). The only way you can make a change like this after filing is by agreement. I suggest it be a written agreement signed by both of you.
This is not legal advice nor is it intended to create an attorney=client relationship. You should not rely on this information. You should consult an attorney directly who can asses and advise you as to your unique situation.
As my colleague indicates, upon the filing and service of the Petition for Legal Separation (or Dissolution for that matter), certain Automatic Temporary Restraining Orders (ATROs) come into effect. One of these ATROs states that there shall be no changes to either party's medical coverage pending the litigation unless there is an agreement between the parties. Should you mutually agree to remove each other from coverage, then you should put that into a stipulation and order, which you each sign, and submit it to the court for the judge's signature and filing (note that unrepresented parties must have their signatures notarized). Once the judge signs it, it becomes a court order. Without a stipulation and order, you may have issues later on if one party changes their mind and alleges there was no agreement.
Disclaimer: This response is based on the limited facts provided. You should consult an attorney for advice based on your specific situation. Responding to your question does not create an attorney-client relationship.