Running deep neural networks for large medical images is a resource-hungry and time-consuming task with centralized computing. Outsourcing such medical image processing tasks to hybrid clouds has benefits, such as a significant reduction of execution time and monetary cost. However, due to privacy concerns, it is still challenging to process sensitive medical images over clouds, which would hinder their deployment in many real-world applications. To overcome this, we first formulate the overall optimization objectives of the privacy-preserving distributed system model, i.e., minimizing the amount of information about the private data learned by the adversaries throughout the process, reducing the maximum execution time and cost under the user budget constraint. We propose a novel privacy-preserving and cost-effective method called PriCE to solve this multi-objective optimization problem. We performed extensive simulation experiments for artifact detection tasks on medical images using an ensemble of five deep convolutional neural network inferences as the workflow task. Experimental results show that PriCE successfully splits a wide range of input gigapixel medical images with graph-coloring-based strategies, yielding desired output utility and lowering the privacy risk, makespan, and monetary cost under user's budget.