If your marriage was initiated properly (and both NYer and I listed many instances when it is not, even though it may be legal from the perspective of the state law) then, even though an adultery is committed, the marriage cannot be annuled and will end with the death of one spouse, correct.
in the bible God gives us permission to divorce in cases of adultery
So does the Church. As I indicated in my previous post, the Church recognizes that some marriages cannot be repaired and allows both physical separation and legal divorce. What it does not allow is re-marriage when a marriage, albeit in a broken state, still exists.
So as I said, if your spouse breaks (ends) the marriage by committing adultery your only recourse according to the Catholic church is to have them killed. :)