Nicely subtle question.
Let me riff on the sentences so you'll see the semantic differences:
- She drank tea with neither milk nor honey.
"Without" negates, so I can flip that around to use "with neither... nor" and keep the same meaning.
- She drank tea without milk and honey... but she did take honey alone.
Of course, most native speakers would say #1 and mean #2, and not notice the difference, but it is there.
The use of "and" ties the two things in the list together, like so:
Pass me the salt and pepper, please
vs.
Pass me the salt, please.