Who is Caroline Bingely talking about when she says "a family trait, I think"; is Caroline talking about Lizzy's family or Mr. Darcy's in Pride and Prejudice by Austen?
I'm referring to the scene where Lizzy is talking to Mr. Darcy about pride and Lizzy says, "Oh dear, I cannot tease you about that. What a shame for I dearly love to laugh."
Excerpt, Pride and Prejudice, Chapter 11
Elizabeth, "Tease [Darcy]—laugh at him. Intimate as you are, you must know how it is to be done.
"Mr. Darcy is not to be laughed at!" cried Elizabeth. "That is an uncommon advantage, and uncommon I hope it will continue, for it would be a great loss to me to have many such acquaintances. I dearly love a laugh. ...
"Follies and nonsense, whims and inconsistencies, do divert me, I own, and I laugh at them whenever I can. But these, I suppose, are precisely what you are without."
Darcy, "[It] has been the study of my life to avoid those weaknesses which often expose a strong understanding to ridicule.[...]
"[..] I have faults enough, .... My temper I dare not vouch for. It is, I believe, too little yielding—certainly too little for the convenience of the world. I cannot forget the follies and vices of others so soon as I ought, ...."
"Implacable resentment is a shade in a character. But you have chosen your fault well. I really cannot laugh at it. You are safe from me."
Having searched the text to confirm my suspicion, I find you have conflated two events and confused the quotations. Above, I've placed an excerpted quotation from the contextual event you identify. In it, as you'll see, Elizabeth actually says:
"Mr. Darcy is not to be laughed at!" cried Elizabeth. "That is an uncommon advantage, and uncommon I hope it will continue, for it would be a great loss to me to have many such acquaintances. I dearly love a laugh."
This occurs at Netherfield after Jane has caught a cold (at her mother's insistence!) and while Elizabeth is there to care for Jane. The entire party, including Jane, is gathered after dinner in the drawing-room. Miss Bingley flirtatiously asks how to "punish" Darcy for a "shocking" commentary on the ladies' motive for walking about the room. Elizabeth says the way to punish a friend is to choose a foible and "Tease him--laugh at him." This leads into the part of the conversation (Chapter 11) you cite as the context of the quote attributed to Miss Bingley: "a family trait, I think," as you put it. Let's jump ahead a bit and sort this out.
Deeper into the novel, in Chapter 45, Elizabeth, along with her Aunt and Uncle Gradiner are sharing hospitality at Pemberley where Darcy is eager to have Elizabeth and Miss Georgianna Darcy become friends. The entire party, including Georgianna, is spending time with Darcy at Pemberley, so Elizabeth is again in company with Miss Bingley. Darcy enters the room and Miss Bingley alludes to the Militia regiment that Wickham was in while stationed in Meryton. This allusion is meant to remind Darcy of the most egregious grievance he might have against Elizabeth and, by extension, her family. Here, Miss Bingley says:
"Pray, Miss Eliza, are not the ____shire Militia removed from Meryton? They must be a great loss to your family."
The import of this statement is, as you now know, to degrade Darcy's opinion of Elizabeth. The meaning of this snide remark suggests how poorly the other girls in the Bennet family behaved in relation to the regiment (flirtation was socially frowned upon as indecorous) and how fond Elizabeth had been (though no longer was) of Mr. Wickham.
So now, let's sort your question out. (1) Your quotations are imprecisely recalled (that's ok). (2) You join two very distant events together in your memory. (3) The context of Miss Bingley's remark is Pemberley on Elizabeth's trip with the Gardiners, not Netehrfield when Jane is ill. (4) Miss Bingley is speaking of the Bennet girls. Now we can answer you specific question of whether Miss Bingley means the Bennet family or the Darcy family. The answer is, technically, neither. The quote is incorrect.
In a conversation in which Darcy has no part, as he has been out of the room, Miss Bingley is speaking to Elizabeth about the Militia and the Bennet family hoping that Darcy will hear, remember their near-scandalous behavior and turn against Elizabeth because, of course, Miss Bingley wants to marry Darcy. She is referring to the Bennets but in a wholly different context and time.