I may be wrong, but I did not think that Illinois is one of the states that provides for deposit of a will while the testator is alive.
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the only thing I can find concerning depositing will with the the state is this new law (effective 1/1/10):
http://www.ilga.gov/legislation/publicacts/fulltext.asp?Name=096-0137
all this does is allow an attorney or directors of an attorney's estate can deposit a will they held with the Illinois Secretary of State. That only applies if the lawyer et.al. cannot locate the testator as well.
Due to that, I would suggest that Illinois has no provision for a typical testator to deposit their will with the courts or any other office within the state government.
I also found this request for release of a will held by the Secretary of state.
http://www.ilga.gov/commission/jcar/admincode/053/053004000000700R.html
In it, you will notice that persons entitled to obtain the will are very limited. You would not have the right to the will without the testators permission or until after his death. I believe this is associated with the law I cited above. It would tend to support the fact that there is likely no way for you to view a will deposited with the state, if there is such a depository available.
So, if you want to see your husbands will, you will have to ask him for a copy of it. I see nothing that would allow you to demand to be allowed to view it.
on top of that, if my wife demanded to see my will against my wishes, I can assure you it would be revised shortly thereafter removing just about everything I could that was directed to be given to my wife.