It can, just be sure if either of you pops off the other remembers to keep paying the premium. Have often seen these lapse as survivor presumed policy was finished and stopped paying it.
Although each person is insured separately each person cannot assign their part of the policy to different lenders.
If you were told a dual life policy will cost you only €4 a month more than your current mortgage protection I bet your current mortgage protection is more expensive than it should be. Get a broker (not your lender) to do a new quote for you. There are dual mortgage protection policies but I don't see the point.