There may be situations when df.reset_index() cannot be used (e.g., when you need the index, too). In this case, use index.get_level_values() to access index values directly:
df['Trial'] = df.index.get_level_values(0)
df['measurement'] = df.index.get_level_values(1)
This will assign index values to individual columns and keep the index.
See the docs for further info.