We study $B_d$ and $B_s$ mixing in unquenched lattice QCD employing the MILC collaboration gauge configurations that include u, d, and s sea quarks based on the improved staggered quark (AsqTad) action and a highly improved gluon action. We implement the valence light quarks also with the AsqTad action and use the nonrelativistic NRQCD action for the valence b quark. We calculate hadronic matrix elements necessary for extracting CKM matrix elements from experimental measurements of mass differences $Δ M_d$ and $Δ M_s$. We find $ξ = f_B_s \sqrtB_B_s / f_B_d \sqrtB_B_d = 1.258(33)$, $f_B_d \sqrtB_B_d = 216(15)$ MeV and $f_B_s \sqrtB_B_s = 266(18)$ MeV. We also update previous results for decay constants and obtain $f_B_d = 190(13)$ MeV, $f_B_s = 231(15)$ MeV and $f_B_s/f_B_d = 1.226(26)$.