This paper proposes a new bivariate competing risks model in which both durations are the first passage times of dependent Lévy subordinators with exponential thresholds and multiplicative covariates effects. Our specification extends the mixed proportional hazards model, as it allows for the time‐varying heterogeneity represented by the unobservable Lévy processes and it generates the simultaneous termination of both durations with positive probability. We obtain nonparametric identification of all model primitives given competing risks data. A flexible semiparametric estimation procedure is provided and illustrated through the analysis of a real dataset.