What is the source for the Midrash that says that in Egypt some babies were put into fields and saved by Malachim who looked like their fathers? Also, what is the context in which the Midrash is taught (Parashah, etc.)?
There is an aggadah in Bavli Sotah 11b that is almost exactly what you're describing. It's in the section that starts with Rav Avira saying that B'nei Yisrael were redeemed from Mitzrayim on account of the righteous women. First they would encourage their husbands in the mitzvah of p'ru ur'vu, then they would stay in their houses while pregnant, and then they would go to the fields to give birth. Hashem then sent malachim to tend the babies in the field. When these children perceived the revelation of Hashem at the splitting of the Yam Suf, they recognised Hashem as the one who had taken care of them in the field and they burst out singing, "This is my God!"
It's possible this aggadah is expanded elsewhere in a later midrash, but the source in Sotah was the first thing that I thought of.
Addendum (added through later edit): Yes, Midrash Rabbah brings this midrash, too. In the Merkin edition (parashah 23, entry 8, on page 264), it begins with Rav Yehudah saying the same thing as recorded in Talmud Bavli Sotah 11b as mentioned above. The midrashic trigger seems to be to explain the pasuk clause, "This is my God," Exodus 15:2. The idea is that saying "this" signifies recognition of something (or someone) previously encountered. Where had they seen Hashem before? When they were babies in the field and Hashem nursed them and took care of them via the malachim who reflected Hashem's splendor.
I still cannot find (or remember) a source saying that the malachim resembled the babies' biological fathers but rather their "Father" in Heaven, Hashem.
(Sorry - I'm working from old fashioned paper sources. Maybe someone else can help with an on-line link.)