I would not do it, OP. It might just be my luck, but most of the families I've worked with, have a *lot* more respect for the nanny than for the housecleaner. Been paid better to.

What would happen when the kid(s) you look after get older and sleep less? When would you fit the cleaning in then?

I am a nanny who also does all housekeeping, I am paid extra each week for it. So far it is working out although it does put some weirdness in the job for me sometimes. Picking up someone's else's dirty socks and cleaning their toilets and toothpaste spit covered sink makes me see them differently, and I will admit it sometimes takes my quality time away from the kids if they don't nap as long as expected or they are having a particularly difficult day and I still have to squeeze in housework, I sometimes clean with a baby on my hip and a toddler 'helping'. It works for us though because mb understands that the house may not always look like a pro cleaned it, but the basic cleaning is always done (bathrooms, kitchen, dusting, and floors in addition to child related cleaning).
So it may not work if your mb wants a pro quality cleaning everytime,sometimes it's just not possible for a nanny to do that.
It's worth asking for a shot with the extra responsibility though, maybe on a trial basis.

OP, before you bring up the issue, I highly recommend that you think this through again and again. Being responsible for a whole house is a HUGE duty along w/caring for young children. Do you really think you can handle it all w/out being overworked?

These parents do not want the quality of care their children receive on a daily basis compromised at all. Perhaps, that is the REASON they have a separate cleaning service.

If you are really sure this is a viable option for you, then by all means bring it up. Also expect to be paid more since you will be providing an extra service to the family.

Hopefully things will work out well for both sides.

Caution:
If they decline, do not take it personally.
They just might not want to have a burned out nanny and do not mind paying the extra bank to hire a maid.

GL.