Most of the answers here are not genre SF; the accepted answer, Around the World in 80 Days, is not science fiction or fantasy at all. Here is an example from genre SF, from a time when interracial marriage was still illegal in some of the United States, in which the interracial relationship is central to the story.
1957: "Pretty Quadroon" by Charles L. Fontenay, first published in If, June 1957, available at the Internet Archive; also at Project Gutenberg. The title, of course, is from the old song "My Pretty Quadroon".
The setting is the Second American Civil War; the protagonist is a Confederate general named Beauregard Courtney:
When the Second War for Southern Independence (the Northerners called it "The Second Rebellion") had broken out, Beauregard had feared it would be a swift holocaust of hydrogen bombs, followed by a cruel scourge of guerilla fighting. But not one nuclear weapon had exploded, except the atomic artillery of the two opposing forces. A powerful deterrent spelled caution to both North and South.
Sitting afar, watching the divided country with glee, was Soviet Russia. Her armies and navies were mobilized. She waited only for the two halves of the United States to ruin and weaken each other, before her troops would crush the flimsy barriers of western Europe and move into a disorganized America.
So the Second Rebellion (Beauregard found himself using the term because it was shorter) remained a classic war of fighting on the ground and bombing of only industrial and military targets. Both sides, by tacit agreement, left the great superhighways intact, both held their H-bombers under leash, ready to reunite if need be against a greater threat.
Just now the war was going well for the South. At the start, the new Confederacy had held nothing of Tennessee except Chattanooga south of the mountains and the southwestern plains around Memphis. That had been on Beauregard's advice, for he was high in the councils of the Southern military. He had felt it too dangerous to try to hold the lines as far north as Nashville, Knoxville and Paducah until the South mobilized its strength.
He had proved right. The Northern bulge down into Tennessee had been a weak point, and the Southern sympathies of many Tennesseans had hampered their defense. The Army of West Tennessee had driven up along the Mississippi River plains to the Kentucky line and the Army of East Tennessee now stood at the gates of Knoxville. Outflanked by these two threats, the Union forces were pulling back toward Nashville before Beauregard Courtney's Army of Middle Tennessee, and he did not intend to stop his offensive short of the Ohio River.
The title character is the general's mistress, a mixed race woman named Piquette:
Piquette's skin was golden, like autumn leaves, with an undertone of rich bronze. Her dark eyes were liquid and warm, and her hair tumbled to her shoulders, a jet cascade. She was clad in a simple white dress that, in the daring new fashion, bared the full, firm swell of her breasts.
Beauregard took her in his arms, and as her lips clung to his he felt a grey old man, as grey as his braid-hung uniform. He held her away from him. In the mirror behind her he saw his face, stern, weather-beaten, light-mustached, with startling blue eyes.
"Piquette, what on earth is this folly?" he demanded, kicking the door shut behind him. "Don't you know I'm moving on Tullahoma in the morning?"
"You know I wouldn't call you unless it was important, Gard, as much as I long for you." When she talked, her delicately molded face was as mobile as quicksilver. "I've found something that may end the war and save my people."
"Dammit, Quette, how many times have I told you they are not your people? You're a quadroon. You're three-fourths white, and a lot whiter in your heart than some white women I've seen."
"But I'm one-fourth Negro, and you wouldn't have married me, for that, even if you'd known me before you met your Lucy. Isn't that right, Gard?"
"Look, Quette, just because things are the way they are...."
She hushed him with a finger on his lips.
"The Negroes are my people, and the white people are my people," she said. "If the world were right. I'd be a woman instead of a thing in between, scorned by both. Can't you see that, Gard? You're not like most Southerners."
"I am a Southerner," he answered proudly. "That I love you above my own blood makes no difference. No, I don't hate the black man, as so many Southerners do—and Northerners too, if the truth were known. But, by God, he's not my equal, and I won't have him ruling over whites."
"This is an old argument," she said wearily, "and it isn't why I called you here. I've found a man—or, rather, a man has found me—who can end this war and give my people the place in the world they deserve."
