What is Multicultural?

So the other day in class when we were discussing our topics for the final research areas, I tried to use the word 'multicultural' to describe people of different religions, cultural backgrounds, as well as races or ethnicities, etc. Every person I used this term with automatically assumed I meant race specifically, and I had to clarify my usage of this term.
Am I really using this term that incorrectly? I see it as two words, multi and cultural. Multi, of course, meaning multiple, many or just plain more than one. Cultural being a reference to the word culture, which I use to mean religions, traditions, races, ethnicities, whether you live in a city or in the country, etc. I do not see race as the only defining factor of a culture, although it certainly is one factor. I use the term with this meaning behind it, but it seems that not everybody has the same definition. Am I being too politically correct because of how I have been taught to be aware of my language use (as we all have in the TE program)? Am I over analyzing this? I suppose I would just like to know when and how the meaning inferred from the use of this word started to change so profoundly? Or am I the one who is confused, and race has always been the primary meaning of 'multicultural'?