This paper presents a novel construction of a Dependent Bivariate Generalized Cox Model to analyze post-shock scenarios in joint life insurance. The Generalized Cox Model, applied by Chaieb et al. [2] to capture the dependency structure of couple's death times in life insurance, was initially developed by Gueye et Jeanblanc [4] to address the limitations of traditional models by incorporating the possibility of events coinciding with shock events. The approach by Chaieb et al. [2] combines individual residual lifetime modeling with the Marshall-Olkin approach to account for catastrophic events affecting both insured individuals simultaneously. Our construction also considers non-simultaneous deaths within a couple following a catastrophic shock, an aspect not addressed in [2]. We propose a method for calibrating the joint survival probability of couples using annuity contract data from Canadian life insurance companies and apply this method to the pricing of joint life insurance products. The results provide significant insights for accurate pricing of life insurance products involving couples.