Mathematical morphology is a technique frequently used in image processing, it has several applications such as segmentation, filtering, compression, edge detection, and feature extraction. Considering this last application here is presented a morphological and convolutional neural network (MCNN) that takes advantage of the different types of morphological operations - erosion, dilation, opening, and closing - by including them in a single layer. Three independent neural networks are used to learn information per channel, Random Forest is used at the end, fed with the three outputs of the NNs. The classification performance of the method was compared against three common CNN architectures: ResNet-18, ShuffleNet-V2, and MobileNet-V2. Two training approaches were used: training from scratch and using transfer learning. A glaucoma classification was conducted using the ORIGA dataset. The MCNN method obtained an AUC of 0.704 (0.672, 0.743 95% CI) with a performance similar to the other CNN methods when trained using transfer learning.