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As NAND flash memory continues to scale down to smaller process technology nodes, its reliability and endurance are degrading. One important source of reduced reliability is the phenomenon of program interference: when a flash cell is programmed to a value, the programming operation affects the threshold voltage of not only that cell, but also the other cells surrounding it. This interference potentially causes a surrounding cell to move to a logical state (i.e., a threshold voltage range) that is different from its original state, leading to an error when the cell is read. Understanding, characterizing, and modeling of program interference, i.e., how much the threshold voltage of a cell shifts when another cell is programmed, can enable the design of mechanisms that can effectively and efficiently predict and/or tolerate such errors. In this paper, we provide the first experimental characterization of and a realistic model for program interference in modern MLC NAND flash memory. To this end, we utilize the read-retry mechanism present in some state-of-the-art 2Y-nm (i.e., 20-24nm) flash chips to measure the changes in threshold voltage distributions of cells when a particular cell is programmed. Our results show that the amount of program interference received by a cell depends on 1) the location of the programmed cells, 2) the order in which cells are programmed, and 3) the data values of the cell that is being programmed as well as the cells surrounding it. Based on our experimental characterization, we develop a new model that predicts the amount of program interference as a function of threshold voltage values and changes in neighboring cells. We devise and evaluate one application of this model that adjusts the read reference voltage to the predicted threshold voltage distribution with the goal of minimizing erroneous reads. Our analysis shows that this new technique can reduce the raw flash bit error rate by 64% and thereby improve flash lifetime by 30%. We hope that the understanding and models developed in this paper lead to other error tolerance mechanisms for future flash memories.