It can make sense to shop for a separate policy for the oldest person. That’s because insurance companies often set their rates based on certain age “bands,” and the age of the oldest person seeking coverage is what counts. So it can be more economical to get one policy for the oldest person in the family and then another (cheaper) policy for the younger spouse (and kids, if they are still dependents). Run the numbers both ways to see.
Another point to keep in mind: if you received health care benefits as part of your spouse’s retirement package from a former employer, your coverage may be affected if he or she dies (Medicare and Medigap aren’t affected at all; each recipient has individual coverage through the programs). Since, it’s up to the plan to set guidelines for coverage of surviving spouses, check with the plan administrator for details.