[1] She is the daughter of an Argentine professional soccer player Jorge Coch and a Mexican mother, Martha Montes de Oca.
In 2006 she attended a casting for the juvenile telenovela Código Postal of the producer José Alberto Castro getting the antagonistic role of Johanna Villarreal, a seductive, clever and envious character where she shared credits with Africa Zavala.
[citation needed] For 2007, Coch started working again with José Alberto Castro with the character of María Inés Castrejón in the telenovela Palabra de Mujer.
[citation needed] In 2008 Ma Pat invited her to participate as Cristina in the telenovela Juro Que Te Amo where she worked again alongside José Ron.
[citation needed] In late October 2011, Jessica was confirmed by the producer Ignacio Sada Madero to star alongside Zuria Vega and Gabriel Soto in the soap opera Un Refugio para el Amor, a remake of the soap opera Morelia, where she played the main antagonist of the telenovela, the same role that was interpreted by former Miss Universe Cecilia Bolocco in the previous production.