There was a serious proposal to build one actually in 1980 as an upper atmosphere research station, half a kilometer or one kilometer in diameter. See Solar Thermal Aerostat Research Station (STARS) and the news story about it in the Washington Post:

"Solar Powered Balloon Station Proposed For the Edge of Space".

For an artist's impression of STARS, see Peter Elson's "Orion Shall Rise" painting, an illustration from Poul Anderson's novel of the same name, Orion Shall Rise, which features the STARS aerostat.

I wonder if it might actually be useful for the high altitude platform to transfer to your orbital airship for JP Aerospace's orbital airships?

Projects To Get To Space As Easily As We Cross Oceans - A Billion Flights A Year Perhaps - Will We Be Ready?

Can You Suggest A Second Earth Apart From Mars?