Post-disaster relief scheduling problem in sustainable humanitarian supply chains (SHSCs) has received increasing attentions from academia. Most existing works focus on the uncertain relief supplies. However, since the destruction caused by disaster can not be estimated accurately and timely, relief demands also can be uncertain. Therefore, in this paper, we study a post-disaster relief scheduling problem in SHSCs considering uncertain relief supplies and demands simultaneously. The objective is to minimize the expected total unsatisfied demand rate, adverse environment impact and economic cost on the upper level decision, and to maximize the expected total survivors' perceived satisfaction on the lower level decision. For the problem, a new stochastic bi-level optimization model is first established. And a hybrid solution approach including a sample average approximation method, a prime-dual algorithm, a linearization technique and a global criteria method is further devised. Finally, a case study is conducted.