I've seen it go both ways with sometimes they seem to understand and other times they don't. So I looked it up in that font of knowledge, Wikipedia:
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MacFarlane has asserted that he and his staff will never take a definite stand on whether Stewie can converse with adults. Whether the other characters understand him or not is left to the writers, who can decide which possibility is most appropriate for a given situation.
Brian is the only character whose ability to understand Stewie is unambiguous; the two generally converse "normally." In one instance, they are apparently able to hear each other's thoughts. Despite this, in the DVD audio commentary for "E. Peterbus Unum", MacFarlane states that adults can understand Stewie, but don't take him seriously, "sort of like... if a 4-year-old who [could] talk told you to **** off." This concept is supported by the other characters often looking at him as he speaks to them, as if to acknowledge him, although paying no mind his often-ungracious addresses, such as calling Lois by her first name (although a few times over the course of the series, he has referred to her as "mother"), referring to Peter as "the fat man", Brian as "dog" or on occasion "Dogbert", and Chris and Meg as simply "you there". The other characters also seem to have blocked out Stewie's odd behavior, though Stewie may be speaking in 'baby' and his lines only come from what he thinks he is saying, and Brian can understand him because he is the only intellectual in the family.
Non-recurring adults often clearly understand the content of Stewie's speech. In Stewie Griffin: The Untold Story the other characters, including "Stu", can understand him.
At the end of the episode "E. Peterbus Unum", there is a self-referential joke relating to this issue. The scene features a class in the distant future watching a "historical" video of events from the episode presented to them and a student asking, "So... can the family understand the baby or what's the deal with that
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http://en.wikipedia.org/wiki/Stewie_Griffin