While it rarely shows in the beginning, these two are the best of friends. Kick-Ass first meets her during an intimidation tactic gone wrong, when he tries to get Rasul to stay away from his then love interest Katie Deauxma. Hit-Girl takes down Rasul and proceeds to kill all of his subordinates before making sure Kick-Ass is ok. During their second meeting, where Kick-Ass also meets her father Big Daddy; the latter tells him that they both like him, even if they don't trust him. Which is high praise from 2 people who spend their time killing crooks. She even went the extra mile and took the taser cartridge that was left behind by Kick-Ass during the Rasul fight to make sure that no authorities catch him. It seems Hit-Girl has more respect for Kick-Ass than Big Daddy does, as he refers to him by his hero name, while Big Daddy calls him "Ass Kick". When Kick-Ass laments his doubts about his heroism, Hit-Girl was dissappointed as she believed he had potential. Even though later on through Red Mist, Kick-Ass becomes responsible for Big Daddy's death, she still insists he work with her to take down the rest of the D'Amico Crime family who killed him. In return for saving him twice, Kick-Ass rescues Hit-Girl twice. Once using Big Daddy's latest weapon, a Jet-Pack Minigun; which he used to mow down the rest of Frank D'Amico's henchmen. The other time using Big Daddy's Bazooka on Frank D'Amico himself. After dropping her off at home they formally introduce themselves by their real names David Lezewski and Mindy McCreedy respectfuly. Marcus, Big Daddy's friend and Mindy's Legal Guardian must have been aware of this friendship, as he manages to register Mindy into David's school, knowing that David would look out for her.
It was implied that Hit-Girl may have some romantic feelings or at the very least a crush on Kick-Ass. While this was played with in the first movie, as upon leaving Kick-Ass' room, she blows him a kiss. The second movie slowly develops it more. At first David denies any Romantic feelings or even sexual feelings or Hit-Girl, he was accused of cheating on her by his now Ex-Girlfriend Katie with Mindy when she catches them talking. (It was really because she was secretly training him to be a better fighter.) However on two occasions Hit-Girl shown some physical attraction to him. The first being during a field-test, when she watches him changing his clothes when putting on a disguise. The second time she reacts to him changing his clothes again only she is too speechless to say anything. When she leaves New York, she gives Kick-Ass a combination of her very first kiss and a goodbye kiss. Kick-Ass is also the only person that Hit-Girl has opened up to on an emotional level as both are fellow superheroes and both had suffered tragic losses. When she was humiliated by her peers in school she goes to his house for comfort over it. She attends his father's funeral and when thugs try to kidnap him, she saves him yet again, killing all but one (The Tumor who was forced to eat his own dick.) It's not all one sided as she is the only person Kick-Ass asks to join his crusade after years of retirment. (the other 2 Battle-Guy and Ass-Kicker simply just followed Kick-Ass.) He's also the only one to honestly tell Mindy that she is beautiful, smart, funny and very strong, which gives her the resolve to get even with Brooke and her henchwomen.
There was only one occasion each movie which gave each other reasons to hate one and other. In the first movie, Hit-Girl showed resentment to Kick-Ass for having Big Daddy Killed. Kick-Ass has reason to resent her for inadvertantly breaking him and Katie up.
Their relationship could also count as this. In the first movie, even though Kick-Ass witnessed what she was capable of, he still treats Hit-girl somewhat like a kid. After Big Daddy's death, he tells her to pack her things (which he assumed was PJ's and a toothbrush.) so she could stay at his house. The tone was no different than a big brother who told his sister to pack up. In the second movie, during the training scene, he refused to hit her on the grounds that she was a 15 year old girl. The latter earned him a slap in the face.