The computer aided diagnosis (CAD) problems of detecting potentially diseased structures from medical images are typically distinguished by the following challenging characteristics: extremely unbalanced data between negative and positive classes; stringent real-time requirement of online execution; multiple positive candidates generated for the same malignant structure that are highly correlated and spatially close to each other. To address all these problems, we propose a novel learning formulation to combine cascade classification and multiple instance learning (MIL) in a unified min-max framework, leading to a joint optimization problem which can be converted to a tractable quadratically constrained quadratic program and efficiently solved by block-coordinate optimization algorithms. We apply the proposed approach to the CAD problems of detecting pulmonary embolism and colon cancer from computed tomography images. Experimental results show that our approach significantly reduces the computational cost while yielding comparable detection accuracy to the current state-of-the-art MIL or cascaded classifiers. Although not specifically designed for balanced MIL problems, the proposed method achieves superior performance on balanced MIL benchmark data such as MUSK and image data sets.