No. Civil unions and marriage are not at all the same. Marriage offers more rights to the parties than civil unions. You do not have to disclose to your partner but your assets could be compromised if any are held jointly ie real estate, bank accounts, etc.
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Civil unions and marriages are not exactly the same, but carry many of the same benefits. However, as you are not married, you will not be entitled to the federal benefits married individuals would have. Your question seems to pertain to the privilege not to disclose statements/confessions to a spouse. I am not an expert on the marital privilege, so without stating whether the privilege applies in your situation, if it did, you would have as much of a right to assert the privilege in a civil union as you would in a marriage in Illinois.
You need to work with a lawyer. You're in over your head. If you already have a lawyer and are trying to find answers on-line, you probably need a better lawyer.
The privilege applies to civil unions. You'll need to properly object to the discovery demand and refer to proper authority. Your lawyer should be able to take care of this for you. If you don't have a lawyer, you need to make some calls.