I think the Hebrew terms for mother - אם em, and father אב av. Klein writes that both of them "probably derive from a child's word", i.e. baby language. Similar sounds are used in many languages. In modern Hebrew we have the terms aba אבא - "dad" and ima אמא - "mom". Klein writes that they come from Aramaic, where they mean "the father" and "the mother" respectively. However, Kutscher points out that in Talmudic Hebrew aba and ima can mean "my/our father/mother". As a proof of this, he brings the story from Pesachim 4a (according to the version of Rabbeinu Chananel), where Rabbi Chiya asked Rav if "Abba" is alive. Rav didn't want to say anything offensive - so he said "Abba" is alive. Kutscher writes that Rabbi Chiya was asking if his own father was alive, and Rav knew that he wasn't. So when Rav said "Abba" was alive, he meant, "yes, my father is alive".
Because of the similar sounds in other languages, it can be difficult to determine if a word in a non-Semitic word that sounds like em or av was borrowed from Hebrew or a related language. However, there are a few examples where this seems to have happened.
For example, the Online Etymology Dictionary claims that the English word "aunt" might be connected to em:
from Anglo-Fr. aunte, from O.Fr. ante, from L. amita "paternal aunt" dim. of *amma a baby-talk or non-I.E. word for "mother" (cf. Gk. amma "mother," O.N. amma "grandmother," M.Ir. ammait "old hag," Heb. em, Arabic umm "mother").While the origin of aunt is questionable, the words "abbot" and "abbey" definitely come from Hebrew. Kutscher, quoted here, writes as follows:
Another instructive example is the use made in Christian times of words derived from the Hebrew אב (av – “father”). In Mishnaic Hebrew we find the Aramaic אבא (abba), the earliest written form of which appears in the New Testament in Mark 14:36. The word followed hard in the wake of the spread of Christianity throughout Europe. In medieval Latin it took the form of abbas, a name for a monk, whence abbatia, a monastery, still retained in French abbaye. Furthermore, by the addition of a Greco-Roman suffix a feminine form was created, abbatissa. In English one finds abbot (and abbess), in German Abt the head of a monastery, in French abbé a priest. Likewise we have in German Äbtissin head of a nunnery by adding in, a German feminine suffix.It is strange that the female head of an abbey would have a title deriving from the Hebrew word for "father" - but that's how language goes!