Since you are in the USA, you may introduce him to other Filipinos as "Ang boyfriend ko ay half-Filipino" or "Half-Filipino ang boyfriend ko." However, that may sound right only if your boyfriend looks Caucasian or can pass for one. If he looks Asian or Filipino, you may have to replace "half-Filipino" with "half-American" (or whatever that half is) to make it sound more politically-correct to the Filipinos you are introducing him to. If you were here in the Philippines, you would say that as, "Ang boyfriend ko ay mestisong-Amerikano", whether he looks Filipino or Caucasian. "Boyfriend/Girlfriend" are the more commonly used terms these days. Some may still use "nobyo/nobya" (from the Spanish novio/novia), but if you want to go pure-Filipino, the term is the genderless "kasintahan".

My boyfriend is half Pinoy.... say it as is, you will be understood. or you may wish to say it in pure Filipino, say - Ang nobyo ko ay may halong Pinoy.

It's "kalahating Filipino" but I don't think we use this term in our everyday lives. Just use "half-Filipino" like in "Half-filipino ang nobyo/boyfriend ko".