We formulate a notion of doubly reflected BSDE in the case where the barriers and do not satisfy any regularity assumption. Under a technical assumption (a Mokobodzki-type condition), we show existence and uniqueness of the solution. In the case where is right upper-semicontinuous and is right lower-semicontinuous, the solution is characterized in terms of the value of a corresponding E -Dynkin game, i.e. a game problem over stopping times with (non-linear) -expectation, where is the driver of the doubly reflected BSDE. In the general case where the barriers do not satisfy any regularity assumptions, the solution of the doubly reflected BSDE is related to the value of "an extension" of the previous non-linear game problem over a larger set of "stopping strategies" than the set of stopping times. This characterization is then used to establish a comparison result and a priori estimates with universal constants.