Their relationship is quite unique. Charlie dated Rose, pre-series and then dumped her. Rose was unable to move on and starts stalking Charlie. Slowly she integrates herself into the Harper family. Charlie bears her and never explicitly prohibits Rose from climbing into their house.
Rose is quite rich too and bails Charlie during a financial crisis, although this was one of her ploys to manipulate Charlie. Slowly Charlie begins to realise his feelings for her when she got "married". Rose is unusually patient with Charlie's flings.
In Season 8, they get married and visit Paris for their honey moon. Charlie died there. It was revealed at his funeral that Rose caught him cheating on her and at a train station, he "accidentally" fell in front of an on coming train. Alan, Evelyn and Berta suspect her of murder, but don't do anything about it.