Jinek was born in Tulsa, Oklahoma and grew up in Washington, D.C., where she attended Sheridan School. Her Czech parents decided to move to the Netherlands when she was eleven. "Just before I went to high school, they decided that they would prefer that my brother and I grow up in Europe. I remember it was six weeks until I spoke my first word in Dutch."
After studying American history at the University of Leiden in 2004, she became foreign editor of the Dutch public network news NOS Journaal, where she covered the United States. In addition, since the end of 2007 she anchored the news show NOS Journaal 3. Since the autumn of 2008, Jinek presented the morning and afternoon news bulletins of the NOS. In May of that year she joined with fellow editor Monique van Hoogstraten, the editor of "Het maakbare nieuws," a collection of eighteen stories with foreign journalists, provided in response to the book "Het zijn net mensen" (Almost Human) of journalist-writer Joris Luyendijk.
She is well known for her coverage of the USA, since her work as a co-host of the show 'Amerika Kiest' (America Votes) of the NOS on the U.S. presidential elections, seen from the Netherlands on November 4 and 5th, 2008. Together with Philip Freriks she reported directly from the Occidental Restaurant near the White House. About the preparation of Amerika Kiest, Jinek told Mikro Guide: "The last weeks before the broadcast Amerika Kiest totally dominated my life, at the end, even 24 hours a day. I was so nervous. It felt like all eyes were on me. I just thought: Oh my god, let me do well. Really well!"
On January 20, 2009, she was the host of the live broadcast on Nederland 1 of the inauguration of Barack Obama as 44th President of the United States.
On March 2, 2009 she was in the news inadvertently when a video of her adjusting her shirt surfaced on the internet. In the video she mutters and shouts mild curses in both English and Dutch. She then exclaims, "Yeah, Boobies!" at one point, continuing with, "Mother of God. Yeah, if you have it, flaunt it!" and citing her mother who might tell her: "I can see your breasts!" She responded the next day, saying she was not annoyed nor embarrassed by the leaked video.
Jinek would be presenting the news show Nieuwsuur (News Hour) with anchor Twan Huys, but her relationship with former criminal defense lawyer Bram Moszkowicz sparked controversy about conflict of interest, and she agreed to decline.
She debuted as radio show host on June 4, 2010, for the program Met het Oog op Morgen (A Glance at Tomorrow), She now hosts the show every Monday night. On August 28, 2011 Jinek presented her last 6 o'clock bulletin for the NOS.
Between 2013 and 2015, Jinek had a relationship with biologist Freek Vonk. The couple separated in May 2015.