No member of Monique's family has actually been seen on the show. But she mentioned her older brother, who apparently got her hooked on professional wrestling (specifically the GWA), in her first appearance, and the Pain King is her favorite pro-wrestler. Her dad apparently likes to play golf, based on dialog in A Sitch in Time.
Nothing is known about Monique's life before she moved to Middleton and transferred to Middleton High School. Kim met her at Club Banana in the Middleton Mall, which is their favorite store, and Monique gets promoted to assistant manager in "Fashion Victim." Sadly enough her last name was never revealed.
Monique seems to dislike Bonnie Rockwaller, Kim's archrival, because of her snobbish attitude.
Romantically, she has a lot of first dates. She describes herself as unable to maintain a relationship, and seemingly seeks a stable relationship with a young man who isn't a total weenie. She was seen getting friendly with Brick Flagg at the end of the Junior prom, but nothing came of it, as he graduated later that year. She recently had to spurn the advances of a smitten Wade, who was rejected because of his age and his decision to use emotion-manipulation on her. Ned seems to be interested, but sadly she's not.
She speaks in initialisms.
Talents and skills
Monique isn't a combatant, and claims to need a good 20 years of training to be any good on a mission. In Kim Possible: A Stitch in Time she does just that, and proves skilled and able; she seems to prefer verbal fights rather than physical fights.
In several episodes she displays a fashion design ability that's on par with The Fashionistas.