Diabetes mellitus and chronic kidney disease are two severe chronic diseases in the world, affecting the quality of a patient's life. However, detecting these two diseases often applies professional medical techniques such as a Fasting Plasma Glucose test and estimating the glomerular filtration rate (eGFR) measurement, which usually requires a blood test. Given the various inconveniences and risks in existing conventional diagnostic approaches, noninvasive healthcare systems based on intelligent electronic detection/prevention are preferred. To achieve this goal, we propose a progressively trainable network, i.e., dual stack network (DsNet), to distinguish patients with chronic kidney disease, diabetes mellitus from healthy people simultaneously through analyzing the facial images of candidates. The first stack subnetwork extracts high-level representative features from the facial images effectively. While the second stack subnetwork can further analyze the extracted high-level features from the first stack subnetwork, before classifying the two diseases from healthy individuals simultaneously. Extensive experiments on a dataset with 229 healthy samples, 236 diabetes, and 200 chronic kidney disease patients show that our proposed method generated the F1-score of 95.33%, 98.17%, and 94.67% for detecting chronic kidney disease, diabetes, and healthy samples respectively. Our proposed DsNet achieves significant improvements compared with other traditional noninvasive detection approaches.