This paper investigates the optimal investment decision for an investor with partial information under the criterion of maximizing the expected utility of terminal wealth. The domestic and foreign stock prices, as well as the exchange rate, are modeled as jump-diffusion processes with stochastic coefficients. By employing Malliavin calculus, we derive a sufficient and necessary condition for the optimal investment strategy in cross-border transactions. In some special cases, a closed-form expression is obtained. Finally, a numerical example is provided to illustrate the impacts of parameters ${\rho }_1$, ${\rho }_2$, and ${\sigma }_R$ on the optimal investment strategy.