Very few women actually appear in The Red Badge of Courage, but Henry does reminisce about several with whom he had gone to school. Henry's mother is also mentioned in retrospect, giving him advice when he leaves home.
“Don't forgit about the socks and the shirts, child; and I've put a cup of blackberry jam with yer bundle, because I know yeh like it above all things. Good-by, Henry. Watch out, and be a good boy.”
When Henry goes to say goodbye to his schoolmates, several young ladies are present.
A certain light-haired girl had made vivacious fun at his martial spirit, but there was another and darker girl whom he had gazed at steadfastly, and he thought she grew demure and sad at sight of his blue and brass.
Other girls appear to admire the newly enlisted soldiers when they stop for meals. One of the novel's most humorous moments comes after the regiment has been called to march.
A rather fat soldier attempted to pilfer a horse from a dooryard. He planned to load his knapsack upon it. He was escaping with his prize when a young girl rushed from the house and grabbed the animal's mane. There followed a wrangle. The young girl, with pink cheeks and shining eyes, stood like a dauntless statue.
The observant regiment, standing at rest in the roadway, whooped at once, and entered whole-souled upon the side of the maiden. The men became so engrossed in this affair that they entirely ceased to remember their own large war. They jeered the piratical private, and called attention to various defects in his personal appearance; and they were wildly enthusiastic in support of the young girl.
To her, from some distance, came bold advice. “Hit him with a stick.”
There were crows and catcalls showered upon him when he retreated without the horse. The regiment rejoiced at his downfall. Loud and vociferous congratulations were showered upon the maiden, who stood panting and regarding the troops with defiance.
Aside from a few references to women by the men, I believe these are the only women who appear in the story.