Unstack dataframe and keep columns

I have a DataFrame that is in a too much "compact" form. The DataFrame is currently like this :

> import numpy as np
> import pandas as pd

> df = pd.DataFrame({'foo': ['A','B'],
               'bar': ['1', '2'],
               'baz': [np.nan, '3']})
  bar  baz foo
0   1  NaN   A
1   2    3   B

And I need to "unstack" it to be like so :

> df = pd.DataFrame({'foo': ['A','B', 'B'],
               'type': ['bar', 'bar', 'baz'],
               'value': ['1', '2', '3']})

  foo type value
0   A  bar     1
1   B  bar     2
2   B  baz     3

No matter how I try to pivot, I can't get it right.