The recent advances of mobile sensing and artificial intelligence (AI) have brought new revolutions in disaster response applications. One example is disaster scene assessment (DSA) which leverages computer vision techniques to assess the level of damage severity of the disaster events from images provided by eyewitnesses on social media. The assessment results are critical in prioritizing the rescue operations of the response teams. While AI algorithms can significantly reduce the detection time and manual labeling cost in such applications, their performance often falls short of the desired accuracy. Our work is motivated by the emergence of crowdsourcing platforms (e.g., Amazon Mechanic Turk, Waze) that provide unprecedented opportunities for acquiring human intelligence for AI applications. In this paper, we develop an interactive Disaster Scene Assessment (iDSA) scheme that allows AI algorithms to directly interact with humans to identify the salient regions of the disaster images in DSA applications. We also develop new incentive designs and active learning techniques to ensure reliable, timely, and cost-efficient responses from the crowdsourcing platforms. Our evaluation results on real-world case studies during Nepal and Ecuador earthquake events demonstrate that iDSA can significantly outperform state-of-the-art baselines in accurately assessing the damage of disaster scenes.