My first son was born when I was 17 years old; so, I have been there. Since you and your boyfriend already live together and have no financial worries I suspect he's having less trouble anticipating twins than you are.
My oldest son was 19 when his son was born and my younger son was only 16 when his daughter was born. If your boyfriend is like my sons, other young males I've known and me; he'll be puffing out his chest like a rooster because "he" fathered two babies at once.
Its a good thing there are no financial concerns that helps a lot, your boy friend will get used to the idea of being a Dad how about you get some books and leave them for him to read,is there a marriage planned that would be a good thing for you ,him and the Babies.There is nothing to prepare him for Fatherhood sounds like hes going to enjoy the Joys early, are both sets of Parents happy with you guys being so young it would be a good thing if ,that now the deed is done, they were Happy and helpful to him and You, Good Luck, keep us up to date as the time goes by.