A 'kind of house' sounds more like 'something that resembles a house but isn't exactly a house'. Somehow it even has some pejorative meaning.
I would think the expression to be used here is something like 'a one-of-its-kind house'... Meaning a 'special house', so pretty much the same as what PieAnne has proposed... But I'm not sure about the '-' dashes in there...
be one of a kind to be very unusual and special: He's one of a kind, he really is. (Cambridge)
be two of a kind If two people are two of a kind, they are very similar: "Patrick and Glyn got on really well, didn't they?" "Yes, well they're two of a kind." (Cambridge)
A phrase you hear a lot in the Uk for this sort of property is 'Architect designed' (makes me wonder who designs the normal houses, just a builder with a bit of string perhaps?)