The field of Medicine and Healthcare has attained revolutionary advancements in the last forty years. Within this period, the actual reasons behind numerous diseases were unveiled, novel diagnostic methods were designed, and new medicines were developed. Even after all these achievements, diseases like cancer continue to haunt us since we are still vulnerable to them. Cancer is the second leading cause of death globally; about one in every six people die suffering from it. Among many types of cancers, the lung and colon variants are the most common and deadliest ones. Together, they account for more than 25% of all cancer cases. However, identifying the disease at an early stage significantly improves the chances of survival. Cancer diagnosis can be automated by using the potential of Artificial Intelligence (AI), which allows us to assess more cases in less time and cost. With the help of modern Deep Learning (DL) and Digital Image Processing (DIP) techniques, this paper inscribes a classification framework to differentiate among five types of lung and colon tissues (two benign and three malignant) by analyzing their histopathological images. The acquired results show that the proposed framework can identify cancer tissues with a maximum of 96.33% accuracy. Implementation of this model will help medical professionals to develop an automatic and reliable system capable of identifying various types of lung and colon cancers.