Parallel machine scheduling problem in multitasking environment plays an important role in modern manufacturing industry. Multitasking is a special scheduling method, in which each waiting job interrupts the primary job, causing an interruption time and a switching time. The existing literatures discuss the problem of multitasking scheduling, however, few studies consider credit risk into such a realm of scheduling models. In this work, we combine customer credit risk into a multitasking scheduling problem. Besides, due to the existence of credit risk and the constraint of deadline of each accepted job, we also consider the job rejection into this problem. To hedge against the worst-case performance (total profit in the worst-case), we then propose a robust stochastic mathematical model with the objective of minimising the maximum difference between total job rejection cost and total revenue. As commercial solvers cannot directly solve this robust stochastic programming model, a sample average approximation model is proposed to further solve this problem. Numerical experiments are conducted to demonstrate the effectiveness of the proposed sample average approximation approach.