The results of recent experimental and epidemiological studies provide evidence on the connection between carcinogenesis, cancer progression, and aging. Existing models, however, are traditionally focused only on one of these aspects of health deterioration. In this paper, we derive a new model of cancer, which describes the connection between the ages at disease onset, the duration of disease, and life span of respective individuals. The model combines ideas used in the two hits model of carcinogenesis with those used in the Le Bras multistate model of aging with constant transition intensities. The model is used in the joint analyses of the US demographic mortality data and SEER data for selected cancers. The results show that the developed approach is capable of explaining links among health history data and provides useful insights on mechanisms of cancer occurrence, disease progression, other aging-related changes, and mortality. Further developments of this model are discussed.