The simple answer is No. Normally insurance is provided to you as a "spouse." Once you are divorced, you no longer are a spouse and therefore are ineligible to continue on the group coverage as a spouse. That is one reason why some parties agree to a legal separation (rather than a divorce) since they remain "spouses" when the process is done.
You do have certain rights to continue your health insurance coverage, at your own expense, through your spouse's employer by enrolling in the COBRA plan. This extension period can range from eighteen months to three years, but there are stringent requirements related to the enrollment period and prompt payment of premiums.
There are also options for CONTINUATION or PORTABILITY coverage which is similar to COBRA but also different. Application for PORTABILITY coverage is made directly to the insurance company and not to the employer. There is no time limitation but there may be a geographic limitation. As in COBRA coverage, there are stringent requirements related to the enrollment period and prompt payment of premiums.
To play it safe, start writing for information before the divorce is signed and make application, in writing, no less than 30 days after the divorce.