I know you wanted to focus on comics, but if we step out of that genre for a second we’ll find that “a bad guy doing good things” is the original usage of the term, minted in 1714

• www.merriam-webster.com/dictionary/antihero

For me personally I’ve always thought of the antihero as either someone who does good but for the wrong reasons or someone who strives for a goal that is good, but uses means that isn’t.
I’d say the Punisher fits the first definition well and Dexter Morgan more the second.