Juices and liquids constituted partly of water, but themselves not pure water, do not create chametz when mixed with flour, according to another set of answers here on Mi Yodeya. Does this same principle apply to milk as well, and can you, therefore, under proper conditions, bake with flour and milk?
A recent Posek, Rav Eliezer Melamed, notes here that kneading with milk would indeed have the status of "Mei Peiros", and would not create Chametz. His source is the Gemara in Pesachim linked below.
There are still a number of other factors to be considered for a Pesak, such as if the milk is watered down, as well as making sure such bread would not fall under any prohibitions, as noted by DanF. Also, see here for an interesting discussion about milk from cows that are fed chametz...
H/t to DoubleAA for sourcing Pesachim 36a as the Talmudic source.
(For those interested, the Gemara, and subsequent Sefaria translation, says:
כדאמר להו ר' יהושע לבניה יומא קמא לא תלושו לי בחלבא מכאן ואילך לושו לי בחלבא והתניא אין לשין את העיסה בחלב ואם לש כל הפת אסורה מפני הרגל עבירה אלא הכי קאמר יומא קמא לא תלושו לי בדובשא מכאן ואילך לושו לי בדובשא
The Gemara adds that this is as Rabbi Yehoshua said to his sons: On the first night of Passover, do not knead for me dough with milk, but from the first night onward, knead my dough for me with milk. The Gemara raises a difficulty: But wasn’t it taught in a baraita: Throughout the whole year one may not knead dough with milk, and if he kneaded dough with milk, the entire bread is prohibited, due to the fact that one will become accustomed to sin, by unwittingly eating it with meat? Rather, this is what he is saying: On the first night of Passover do not knead me dough with honey; however, from then onward, knead me dough with honey.)