In this paper, we propose a model for pricing the vulnerable European options when the value of the firms asset of the counterparty follows a double exponential jump-diffusion process and correlates with the underlying asset value of the option. The two-sided jump process can model sudden down and up changes in the firms asset value, which provides more economic insights on vulnerable options pricing. Incorporating the early default and payoff conditions, and based on the explicit formula of the joint Laplace transforms of the first passage times for the two-sided jump process and a correlated Bownian motion derived by us, we present a simple analytical pricing formula for vulnerable options via two-dimensional Laplace transforms, one for the space and one for the time, and the formula can be implemented by numerical Laplace inversion. The numerical results show that our pricing formula is correct and efficient.