Want to ask a different question?
Great question.
It depends a great deal on the specifics of your policies. The good news is that this is a question that Human resources departments receive ALL THE TIME, so they should be well versed in explaining the benefits and costs of having your coverage be extended to your spouses and vice versa.
Frequently, covering family members will require that money be withheld from your paycheck to cover the added premiums, even if you are covered at no cost to you. Sometimes, family members are covered only if other insurance isn't "available" to them.
Give your HR department a call, and once you're given the specifics, feel free to follow up here if you have questions.