Converting a pandas multi-index series to a dataframe by using second index as columns

You just need to unstack your series:

>>> s.unstack(level=1)
second       one       two
first                     
bar    -0.713374  0.556993
baz     0.523611  0.328348
foo     0.338351 -0.571854
qux     0.036694 -0.161852