Really.
Dunmer heritage tends to show. You know, dark skin, red eyes and such. Martin's as human as one gets to be in Tamriel.
Barenziah is about 500 years old. During which time she had what? Five partners? That's one every 100 years on average. Most people do much worse by the standards you judge her.
Actually she used to be a "camp follower" so it was a -lot- more than five. We should remember though that elves tend towards promiscuity in early life but end up very monogamous --> Once she settled down with Symmachus, he was her only partner for several -hundred- years. That's some pretty amazing devotion. And if she was tempted by the Nightengale, well, we are dealing with a Master of Illusion here...he may have charmed her so as to get the Staff.
Also, Helseth is definitely Symmachus' child, as is Morgiah. I suppose the third child (with Tharn) would have been born in Wayrest, but I've never heard anything about him/her.
And Olivia - good call on the Dunmer heritage. Children take the appearance of their mothers.