For being a powerful magical artifact, Death's Cloak of Invisibility sure does have a lot of catches and rules.
Xenophilius Lovegood describes it as a Cloak that "really and truly renders the wearer completely invisible, and endures eternally, giving constant and impenetrable concealment, no matter what spells are cast at it" (411).
Yet, this statement is a little misleading and confusing. It means simply that the Cloak itself cannot be damaged by spells, not that the wears are immune as well.
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However, there are multiple instances where Harry is frozen while invisible underneath the Cloak. First, Draco's spell, then later Dumbledore's.
Perhaps most importantly though, Harry acknowledges hiding underneath it could not have saved his family: "The Cloak couldn't have made them curse-proof" (715).
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Tune in tomorrow for J is for J.K. Rowling!