We find a class of flat supersymmetric brane-antibrane configurations. They follow from ordinary brane-antibrane systems by turning on a specific worldvolume background electric field, which corresponds to dissolved fundamental strings. We have clarified in detail how they arise and identified their constituent charges as well as the corresponding supergravity solutions. Adopting the matrix theory description, we construct the worldvolume gauge theories and prove the absence of any tachyonic degrees. We also study supersymmetric solitons of the worldvolume theories.