Humanoid robots are often supposed to share their workspace with humans and thus have to deal with object used by humans in their everyday life. In this article, we present our novel approach to humanoid navigation through cluttered environments, which exploits knowledge about different obstacle classes to decide how to deal with obstacles and selects appropriate robot actions. To classify objects from RGB images and decide whether an obstacle can be overcome by the robot with a corresponding action, e.g., by pushing or carrying it aside or stepping over or onto it, we train and exploit a convolutional neural network (CNN). Based on associated action costs, we compute a cost grid containing newly observed objects in addition to static obstacles on which a 2D path can be efficiently planned. This path encodes the necessary actions that need to be carried out by the robot to reach the goal. We implemented our framework in ROS and tested it in various scenarios with a Nao robot as well as in simulation with the REEM-C robot. As the experiments demonstrate, using our CNN the robot can robustly classify the observed obstacles into the different classes and decide on suitable actions to find efficient solution paths. Our system finds paths also through regions where traditional motion planning methods are not able to calculate a solution or require substantially more time.