|א וַתְּדַבֵּר מִרְיָם וְאַהֲרֹן בְּמֹשֶׁה, עַל-אֹדוֹת הָאִשָּׁה הַכֻּשִׁית אֲשֶׁר לָקָח: כִּי-אִשָּׁה כֻשִׁית לָקָח.||1 And Miriam and Aaron spoke against Moses because of the Cushite woman whom he had married; for he had married a Cushite woman.|
Thus, he rejects the standard midrashic peshat that the Kushite woman was Tzipporah because a) we would already know that Moshe married Tzipporah, so why does the Torah go out of its way to tell us כִּי-אִשָּׁה כֻשִׁית לָקָח, and b) Midian is not equal to Kush. Thus, he uses realitistic, narrative-based objections to explain why he does not adopt the midrashic explanation. (This may play in to the theme I've been emphasizing recently -- that is, otherwise others, or Rashbam himself, would consider the midrash on the level of historic reality, as opposed to allegory - if all midrash is allegory, why bother rejecting is on these realistic/narrative grounds.)
More curious is the explanation he labels the primary peshat. That is that the Kushite woman Moshe married was a queen of Kush, for between leaving Egypt and arriving in Midian, for 40 years, Moshe went to Kush and married a Kushite queen. He never slept with her, but Miryam thought that he did, and this was what she complained about. His source for this is a sefer called divrei hayamim leMoshe Rabbenu.
Here is this work, The Chronicles of Moses Our Teacher. It is a fairly short read, and it is filled with legendary midrashic material. (It also occurs in one of the many Sefer HaYashars.) Yet Rashbam is willing to accept its account as peshat, and as the primary peshat. Perhaps he considered it an extra-Biblical source of somewhat ancient origin, and the cryptic statement of כִּי-אִשָּׁה כֻשִׁית לָקָח was referring to an event we would otherwise not have known about if not for this external tradition.
I would have said that rather, this midrashic source saw the gap from Moshe's leaving Egypt to Moshe's return at around age 80, and saw the cryptic Isha Kushit, saw one can interpret Isha as noblewoman, and expanded from there.
But anyhow, we see that a pashtan such as Rashbam is willing to accept this midrash as a literal account of what happened, and in fact as the primary peshat.