Raised between Ethiopia and Vietnam, Jernberg moved to Sweden for choir school at age 10. While there, as she told The Wire, she discovered interests outside the Western choral tradition — Tuvan throat singer Sainkho Namtchylak, Sidsel Endresen, Phil Minton, Diamanda Galás. In the years since, she has experimented with split-tone singing, pitchless singing and distorted singing. A commission for the Norbotton Big Band and a 2012 collaboration titled Music Inside the Language both found her borrowing from various dialects and text-sound composers, although her solo work increasingly abstracts language from meaning.

As an improviser, Jernberg appears most frequently with cellist Lene Grenager; as a composer, her focus lies in the blending of improvisation and composition. She co-directs and writes for modern jazz octet Paavo and contemporary quartet The New Songs. In addition to creating works for her own groups, she has also recently been commissioned to create works for chamber ensemble DuoEgo and The Peärls Before Swïne in Sweden, Norway's Trondheim Jazz Orchestra, and The Opera Group in the UK.

With Montreal's Fire! Orchestra, Jernberg has released two albums, Exit! and Enter, and is at work on a solo LP with percussionist Mats Gustafsson. She currently splits her time between Oslo and Stockholm.