Charlie always seems to be the same kind of guy and father. He clearly loves Bella, but has no clue what's going on in her life, or so it seems at least. According to Edward, Charlie is more perceptive than Bella gives him credit for. He just doesn't want to know the truth, because it's usually connected with strong emotions. He shuns dealing with any kind of emotional situation. That's why, whenever his role as a father calls on him to have "a talk" with Bella, he clearly suffers through the whole thing.
After Edward's return, Charlie tries everything to prevent Edward and Bella's relationship from becoming too serious. He encourages her to go out with other friends. Big giant hint: Jacob! Deep down, he seems to know about the state of affairs between Bella and Edward, because he gathers all his courage to have a "sex talk" with Bella. It's short and awkward, but he does his duty. At the end of Eclipse, he also reveals to her that he believes she'll be leaving him soon. Again, though, he doesn't try to stop her: "Just give me some advance notice. Give me a chance to hug you goodbye" (26.95).
On the other hand, when Jacob kisses Bella, Charlie even congratulates Jacob on doing so. He even defends Jacob in front of Bella, saying that he's just a teenager. It's obvious that he believes that Jacob is the better choice for Bella, but he's not the kind of father to tell her what to do. He wants her to make her own choices and all the confusion that comes with it: "Sometimes the right thing for one person is the wrong thing for someone else. So good luck figuring that out" (16.204). Although he often thinks he's not a good father, Bella promises him that he's a great dad.
For more info on Charlie, check out his "Character Analyses" in Twilight and New Moon.