Mel-vegetarian

NOUN/ADJECTIVE: A vegetarian who abstains from consuming meat, dairy, and eggs, but still consumes honey. Thus, a vegan who still consumes honey is in fact a "mel-vegetarian".

NOUN: The practice of abstaining from the consumption of all meat and animal products, with the exception of honey.

There are 4 types of vegetarians: lacto-ovo (dairy and eggs), lacto (dairy), ovo (eggs), and mel (honey). The other types of vegetarianism don't necessarily need to incorporate "mel-" into their name, as "mel" is used for only particular circumstances where it is necessary to distinguish.

mel-vegetarianism (noun)
mel-vegetarians (plural noun)

Variations: mella-vegetarian (plural usage of "mel"), melli-vegetarian, melle-vegetarian, mello-vegetarian, meltarian, mellatarian, mellitarian, melletarian, mellotarian, etc.