Split cards have 2 Converted Mana Costs everywhere except the stack. I saw a similar question relating to Dark Confidant explaining that you lose life for each converted mana cost, however the way it was explained (you get 2 answers) made me unsure if you can counter a spell with either converted mana cost, or the sum of the converted mana costs.
If the spell has converted mana cost 1 or 2, it will be countered.
With Dark Confidant and Life // Death, you lose 3 life. This is not because Life // Death has a converted mana cost of 3, but because Dark Confidant receives both answers (1 and 2) and reacts to each of them.
Counterbalance is a positive comparison: does the revealed card have the same converted mana cost as the cast spell? The converted mana cost of Life // Death is both 1 and 2, so if the revealed card has that a mana cost of either 1 or 2 then the answer to the question is yes, and the spell is countered.
So, results that receive more than one answer apply to each of those answers. Positive comparisons that receive more than one answer use the or comparison (one or more "yes" = "yes"). Negative comparisons (rule 708.6b) use the nor comparison (one or more "yes" = "no).
In the library, Life // Death has CMCs of 1 and 2. If the spell cast has a CMC of 1 or 2, it will be countered.
This is similar to how Protection from Red will protect from a source that's Red and White, or how a Human Soldier will get +1/+1 from Field Marshal.