Let's pick a male. He marries a Cro-magnon female. His kids get half his nuclear genes. How much of his mtDNA do they have? Not one of them has any.Let's pick a female neandethal who marries a Cro-magnon male. Again, her kids each get half of their nuclear DNA from her. How much of their mtDNA do they have? All of them have all of it. "Now we're cooking!" you say.
But let's be real and say half of her brood is male. None of her granchildren from them will have neanderthal mtDNA. It's only her direct female line that will carry the mtDNA. She's only one woman in a village with maybe ten women in it, and the Cro-magnons think she's butt-ugly.
Marriage? Into another species? Isn't that sort of like you marrying a dog or a cat?
Would you let your daughter marry a dog or a cat?