Since then, she has gained the most attention for her battles with National Ministers over her dress sense.
Mrs Turei said Dr Norman's higher profile was not related to performance, but to the issues he covered.
"Russel is responsible for economic issues, and that tends to dominate the political discourse," she said. "It comes and goes. It did with [previous leaders] Rod and Jeanette. It just depends on the issues of the day."
Asked whether she had been overshadowed by her colleague, she said: "No... I have made sure that inequality and child poverty are on the political agenda."
Her strengths are in "being out and about". Unlike many MPs, Mrs Turei "loves campaigning". She has begun door-knocking and promoting some of their policies to the public, such as putting a nurse in every low-decile school and the expansion of cycleways and walkways around schools.
Mrs Turei and Dr Norman will mark five years as co-leaders this weekend. With the election four months away, they now have their eyes on Cabinet positions.
Mrs Turei wants a significant social portfolio - housing, education, or social development. But if Greens are part of Government, she will not rule out taking on a position outside of Cabinet which focuses on looking after internal party issues.
She said getting into Government, and then Cabinet, will require a strong relationship with Labour.
That relationship suffered a setback last month when Labour turned down a Green proposal to campaign together. Mrs Turei downplayed Labour's rejection of a formal agreement, saying the voters still saw the two parties as natural coalition partners.
"We thought our position was the right tactical move to make. They chose differently.
"My purpose now is to present to the country a vision of what Greens in Government will deliver... Everybody will understand that to be a Government which includes Labour."
But the Green Party was still be eager to cement the relationship. Mrs Turei said the leadership wanted to invite Labour leader David Cunliffe to speak at this weekend's conference as a symbolic gesture of unity. This plan was scrapped because the party membership had not yet decided who Greens would align with in any coalition talks.
Green ministerial positions could also be contingent on whether New Zealand First was part of a Labour-Greens coalition.
Greens would be nervous about getting frozen out of Cabinet, as they were in 2005 when Labour and New Zealand First formed a government.
"I just don't see that that's likely," Mrs Turei said. "The circumstances that led to that in 2005 just don't exist now... We get on better with New Zealand First than we ever have."
The party was also bracing for election-year attacks from National on Greens' credentials.
Mrs Turei believed there was no longer "fertile ground" for these attacks. Green policies such as state-subsidised housing insulation had been adopted by National and proven to be successful.
"People aren't frightened of the Greens," Mrs Turei said. "They are behaving in a more sustainable way in their individual lives, so seeing that reflected in politics is perfectly normal and right."
