A midrash is a form of commentary that attempts to interpret the Bible. Matthew used midrash aggada, a form of story-telling ("Aggada" means "story" or "telling" in Hebrew). Jewish midrashim are often fanciful, but it is not required of the faithful that the literally believe any one midrash. If a better midrash is found, then Jews were permitted to switch allegiances and accept the newer midrash as a true explanation of a biblical text.
How many passages unique to Matthew should be termed Christian midrash depends on how broadly we define the term. Certainly, John Shelby Spong calls Matthew's story of the magi, or wise men, Christian midrash. The flight to Egypt, Herod's Slaughter of the Innocents and the journey from Egypt to Nazareth are equally clearly midrash.