I don't understand the hatred for the OP. This is a totally legit question. When someone spends 5 days a week in your house and sees you and your family together in various situations, but you never see that person in their house or with their family members, it does feel a little uneven.
OP, I think it's good (as others mentioned) that your nanny is discreet. It's professional of her to keep her private life to herself, and you should appreciate that.
But it does seem like an odd relationship, particularly if you didn't grow up with a situation like this. The relationship is very intimate on one level -- she's almost like a family member, but she's not. It feels like with all the care she is giving to your children (which naturally involves knowing some things about your family, like where you work and where you go on vacation and how you like to spend your time), you should reciprocate because that's what you would do with any friend or family member. But you can't/shouldn't because you are paying her to do this. It's just awkward, and you have to live with it (and so does she).
There is a ton you can read into people's lives without snooping. If you hear MB and DB talk when they come in the door or hear them on the phone, you can tell a lot about them. Or if the kids say something about mommy or daddy doing something or not. Or you can tell a certain level of preference and philosophy from the type of products they buy and the way their house looks and what they ask you to do with their children. Heck, I'm not a nanny, but I know these things about some of my good friends who have kids, and I only see them at drop-off and pick-up at our preschool and on some playdates!