This paper investigates the a posteriori analysis of Branch-and-Bound (BB) trees to extract structural information about the feasible region of mixed-binary linear programs. Using only the branching decisions of a tree and one dual bound per node, we introduce three polyhedral outer approximations of the feasible region, namely a disjunctive, a network-flow-based, and a mixing-set-based approximation. We show that they are the projections of the convex hull and of two continuous relaxations of a single mixed-binary set, and that they form an inclusion hierarchy. Separating over the network-flow-based and the mixing-set-based approximations reduces to a minimum-cost flow problem and to a maximum flow problem on a network obtained from the tree. Both are solved in strongly polynomial time, and their optimal dual solutions provide separating inequalities. We further introduce star tree inequalities, which generalize the strong-branching inequalities of Kılınç et al. to BB trees of arbitrary depth and are separated in strongly polynomial time. Finally, we show that every inclusion of the hierarchy can be strict.