They were brothers. Well they weren't brothers by blood. But that didn't matter because they were brothers, even if they didn't look alike or came from the same mother. They were brothers.
They had all been adopted from an orphanage by the greatest person in the entire world "treville". He had become their father. The father none of them ever had.
You see both Porthos and Artemis had been left by their mothers at the orphanage when they were babies.
Athos' little brother had died when he was 7 (car accident) and his mother had blamed him (yeah she because a 7 year old can drive a car, crash it and kill his baby brother) so his mother didn't want anything to do with him. So one day she just left him at the orphanage.
Charles' mom died giving birth to him and his father was murdered when he was 4 (yeah none of them had the easiest childhood)
So when treville came to the orphanage one day saying he wanted a to adopt a boy. Let's just say Porthos, Athos, Artemis and Charles weren't called the "inseparable" for no reason. Long story short he left with 4 very happy kids