A milaaya could refer to a bedsheet or a long headwrap worn by women (at least in Egypt). From the context you laid out it appears that it is referring to the latter. I tried to find a picture of one, but did not have much luck.
As Josh said, الملاية -also called الملاية اللَف- (rapping melaaya) is a piece of black cloth that women from popular classes used to wear till a few decades ago.
You can see it in many classical Egyptian movies.
It is considered part of the folklore and, in the past few years, has become part of the belly dancers' dresses (specially foreigners) . Like you can see here.