In truth, Scout has probably never really thought of Calpurnia as being a real "Negro" until she accompanies her to the First Purchase African Methodist Episcopalian Church on the other side of town one Sunday. For Calpurnia has always been an integral part of the Finch home and a surrogate mother for the children; furthermore, she has always spoken just as the Finches do.

Now, at a poor church that has no ceiling or hymn books, Calpurnia speaks as though she were one of these poor people of color. She even bristles and challenges the tall Lula in a bellicose manner. Seeing Calpurnia in this setting causes Scout to bridge the two areas in her mind, whereas before the black section had been a strange world into which no one she has ever known has entered other than her father. Certainly, it is an important moment in Scout's and Jem's maturation.

This experience on the other side of town enables Jem and Scout to perceive not only Cal in a new light, but also the community of people of color. Such new perceptions of Scout give her an understanding and sympathy for these people. When the music begins, Scout listens as

...the people chimed in, and the music swelled all around every corner: "And we only reach that shore by faith's degrees...." 

Jem and Scout have attained a "new grace," the grace to see and appreciate where Calpurnia's relatives and friends live. Also, from Cal they have learned "...that it is not necessary to tell everything you know."

The passages you are looking for are in chapter 12, when Cal brings Jem and Scout to her church.  When Calpurnia is at their house, she speaks "normal", or at least, like other white southerners in the city of Maycomb.  But when they all get to the church, and Calpurnia is around other black people, Cal starts speaking the Negro dialect again.  This startles Scout, and opens her up to the fact that Cal might be more than just their housekeeper; she might actually live a real life outside of when Scout sees her.  Scout thinks to herself,

"That Calurnia led a modest double life never dawned on me.  THe idea that she had a separate existence outside our household was a novel one, to say nothing of her having command of two languages."

So, Scout is impressed that Cal has a life outside their home, AND that she can speak 2 langauges so well.  It isn't really two languages, but she feels like it might as well be.  At the church, Cal slipped back into the Negro dialect, and Scout found it unusual that she did so, but it led to a rounding out of Cal's character for her.