Superfecundation

Superfecundation is the fertilization of two or more ova during the same ovulatory cycle, by separate coital acts. When the fertilization is by sperm from different fathers, it is called heteropaternal superfecundation.

In other words, fraternal twins can have different fathers.

According to this article in the medical literature, approximately 1 in 12 sets of dizygotic (fraternal) twins result from superfecundation.

The same paper (1993) estimates that 1 in 400 sets of fraternal twins born to married, white American women result from heteropaternal superfecundation.

Heteropaternal superfecundation has been suggested as an explanation for the "black and white" twins I wrote about here. There's been no official word on the mother's sexual history, or whether paternity tests were done, so it remains speculative.

And maybe the twins who married each other without realizing they were related had different fathers, and were merely half-siblings. Although I doubt that would have been much consolation.