Workflow scheduling is a long-studied problem in parallel and distributed computing (PDC), aiming at efficiently utilizing compute resources to meet user's service requirements. Recently proposed scheduling methods leverage the low response times of edge computing platforms to optimize application Quality of Service (QoS). However, scheduling workflow applications in mobile edge-cloud systems is challenging due to computational heterogeneity, changing latencies of mobile devices and the volatile nature of workload resource requirements. To overcome these difficulties it is important, but at the same time challenging, to develop a long-sighted optimization scheme with efficient modelling of the QoS objectives. In this work, we propose MCDS: Monte Carlo Learning using Deep Surrogate Models to efficiently schedule workflow applications in mobile edge-cloud computing systems. MCDS is an Artificial Intelligence (AI) based scheduling approach that uses a tree-based search strategy and a deep neural network based surrogate model to estimate the long-term QoS impact of immediate actions for robust optimization of scheduling decisions. Experiments on physical and simulated edge-cloud testbeds show that MCDS can improve over the state-of-the-art methods in terms of energy consumption, response time, SLA violations and cost by at least 6.13, 4.56, 45.09 and 30.71 percent respectively.