Have been trying to figure it out all day including Google search.
An English young married couple.
He is tall dark and handsome.
It must have been made in the 80s but it was set in the 20s/30s/40s.
Sorry that's a wide brief.
They would not be obvious detectives and would get involved with crimes to work out what was going on
I remember one scene where they checked into a hotel as Mr and Mrs Smith (obviously not Pitt/Jolie!).