In "Desiree's Baby" by Kate Chopin, the setting is an important aspect of answering this question. Although none of this information is stated, the reader has to make inferences based on the details of the story. This story takes place prior to the American Civil War [There are slaves on Armand's plantation] and in the state of Louisiana [There are bayous mentioned and French is spoken], which is in the deep South.
The marriage between Armand and Desiree initially was based on deep love. Armand was told that Desiree's heritage was unknown, but it seemed to make no difference to him when he looked at Desiree.
When their child is born, no one could tell that the child was of mixed race. As he grew older, his negroid features began to develop, and it was apparent that one or the other parent had to have black ancestry.
Desiree asks Armand despairingly, "Tell me what it means!"
'It means,'he answered lightly, 'that the child is not white; it means that you are not white.'
Later, of course, it is learned that Armand is the one with the Negroid ancestry and not Desiree.
At the time of the story, no marriage between the races would have been accepted in the upper class society of the Valmondes and the Aubignys. The black people were slaves. Sometimes the white owners would have sexual relations with a black slave woman, which is apparently how Armand was born. The black features sometimes skip generations. Armand apparently looked white, but his son had received some of the black features. The marriage would have been disavowed by both families if it had been known that either the bride or the groom was a mulatto [bi-racial].
Today, times are different. In America, it has become more acceptable for black and white people to marry. This is not true everywhere, particularly in the midwest [or what is called the "Bible Belt"] where standards for mixing of the races are still not encouraged.
Certainly, black and white people are friends, and the barriers have for the most part been eradicated. However, it depends on where a person lives. If a black and white racial couple were seen in Los Angeles, no one would notice. As seen on television, many celebrities and others have racially integrated marriages.
On the other hand, if a mixed race couple were to walk down the streets of a small town in the midwest [and maybe still some places in the south], staring and gossiping would run rampant. It does not make it right, but that is the way it is in some places.