The Russian term for the partial floor located on the third level in the picture is мезонин (mezonin), but in English mezzanine is used to designate something different - an intermediate floor in a building.
So what do we call this kind of structure (in the picture) in English? This kind of structure is traditional for Russian houses of the 19th century, and it's always positioned in the middle of the roof, henсe its name.
Here's another example of Russian мезонин: