We have examined the interstellar scintillations of the pulsars in the double pulsar binary system . Near the time of the eclipse of pulsar A by the magnetosphere of B , the scintillations from both pulsars should be highly correlated because the radiation is passing through the same interstellar plasma . We report confirmation of this effect using 820 and 1400 MHz observations made with the Green Bank Telescope . The correlation allows us to constrain the projected relative position of the two pulsars at closest approach to be 4000 \pm 2000 km , corresponding to an inclination that is only 0.29 \pm 0.14 ^ { \circ } away from 90 ^ { \circ } . It also produces a two-dimensional map of the spatial correlation of the interstellar scintillation . This shows that the interstellar medium in the direction of the pulsars is significantly anisotropic . When this anisotropy is included in the orbital fitting , the transverse velocity of the center of mass is reduced from the previously published value of 141 \pm 8.5 km s ^ { -1 } to 66 \pm 15 km s ^ { -1 } .