It only protects Harry from Voldemort.
When Voldemort took Harry’s blood into his body, he took Lily’s enchantment into himself as well - but that enchantment is a very specific one. It only protects Harry from Voldemort. It does not offer protection to anyone else, even if they take Harry’s blood, because it was specifically created to save Harry from Voldemort.
“He took into his body a tiny part of the enchantment your mother laid upon you when she died for you. His body keeps her sacrifice alive, and while that enchantment survives, so do you and so does Voldemort’s one last hope for himself.”
- Harry Potter and the Deathly Hallows, Chapter 35 (King’s Cross)
On her old website, JKR explicitly stated that by taking Harry’s blood into himself, he is keeping alive Lily’s protection over Harry. It only tethered Harry to life. The only thing it could do for Voldemort is heal him more fully if he chose to feel remorse.
Having taken Harry’s blood into himself, Voldemort is keeping alive Lily’s protective power over Harry. So Voldemort himself acts almost like a Horcrux for Harry – except that the power of Lily’s sacrifice is a positive force that not only continues to tether Harry to life, but gives Voldemort himself one last chance (Dumbledore refers to this last hope in chapter 35). Voldemort has unwittingly put a few drops of goodness back inside himself; if he had repented, he could have been healed more deeply than anyone would have supposed. But, of course, he refused to feel remorse.
- F.A.Q. on J.K. Rowling’s old website
The enchantment only protects Harry. Therefore, having Harry’s blood and Lily’s enchantment would do nothing to protect Voldemort from death, just as Harry having a piece of Voldemort’s soul in him does nothing to protect Harry from death.