Jude's father and Sue's mother were siblings. The Aunt who raised Jude was his maiden great-aunt.
It's easy to miss, but the very first mention of Sue, long before she became a major character, was way back in Chapter 2 when Jude's Aunt Drusilla mentioned her as his cousin:
“I’m sure he couldn’t ha’ took a better one. The boy is crazy for books, that he is. It runs in our family rather. His cousin Sue is just the same—so I’ve heard; but I have not seen the child for years, though she was born in this place, within these four walls, as it happened. My niece and her husband, after they were married, didn’ get a house of their own for some year or more; and then they only had one till—Well, I won’t go into that. Jude, my child, don’t you ever marry. ’Tisn’t for the Fawleys to take that step any more. She, their only one, was like a child o’ my own, Belinda, till the split come! Ah, that a little maid should know such changes!”
The phrase "My niece and her husband" suggests that Sue's mother is the one who was a blood relative to Jude and Drusilla. In Chapter 11, we get a little more information:
“Going to ill-use me on principle, as your father ill-used your mother, and your father’s sister ill-used her husband?” she asked. “All you be a queer lot as husbands and wives!”
“Aunt—did my father ill-use my mother, and my aunt her husband?” said Jude abruptly, sitting down by the fire.
“It was the same with your father’s sister. Her husband offended her, and she so disliked living with him afterwards that she went away to London with her little maid. The Fawleys were not made for wedlock: it never seemed to sit well upon us. There’s sommat in our blood that won’t take kindly to the notion of being bound to do what we do readily enough if not bound. That’s why you ought to have hearkened to me, and not ha’ married.”
Sue is, presumably, "her little maid".
Meanwhile, Aunt Drusilla is referred to as a "maiden aunt", and also as his "great-aunt" and as an aunt to both him and Sue. She is presumably the sister of one of Jude and Sue's shared grandparents, and certainly not the mother of either Jude or Sue, although Sue was born in the house where she lived, since her parents weren't able to get a house of their own at that time.