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Share of freehold. The owners of the two flats jointly owned the building then each had a lease with what they were responsible for. It worked out very well, in part because the leases split the building up so there was very little joint expenditure (for instance I was responsible for the roof which worked out well when I wanted to add a loft conversion). Also got along well with the guy downstairs so we each did bits and pieces as and when (repainting communal areas, front yard, etc)
@stevo_com I know a couple of people who do that. It seems weird, you can't rebuild only half a house.
@aggi that sounds ideal. Was it leasehold?