A broken home is one in which the parents no longer live in it together. they could be divorced or only separated, but if mother and father choose to live apart from each other, the home is broken.
A girl or boy from such a home is not considered “second class” as you put it, BUT that being said, many people are leery of shidduchim where the boy or girl may have observed some very unpleasant interactions between the parents, as they were growing up, which could impact on their ideas of how home life should be conducted.