compared to today there wasn't typically the time for box sets in the early 80's and only occasionally boxes were released.
Regarding The Who there was only one box set released in the 80's. It's called Phases and came out in May 1981.
The box contains 9 Who LP's
A Quick One
The Who Sell Out
Live At Leeds
The Who By Numbers
Who Are You
and has cat.no. Polydor 2478144.
Though the box has not really a black and white cover, it has a mono-color photograph.
This was the only Who box which was put out around that time and for years. So this must be definitely the one you're searching.
It's slightly difficult to find one and it's mean value is in the region of 100 Euro.