*There* sentences are difficult in any language. I'd say there are several options, each has its merits.
1. I believe modern linguists would call *there* the subject.
2. You could say *there is/are* are exceptions, in that subject and verb are allowed to disagree.
3. You could say *is* in the case of *there is a man and a woman* is ungrammatical, and that it should always be *are* in this case (modern linguists will hate this).
4. You could say *there is a man and a woman* consists of *two* clauses, one elliptical, as in: *there is a man and [there is] a woman*.