Intense, asymmetric 1ω+2ω laser fields are used to affect the directional ejection of multiply charged ion fragments from a variety of molecules, including N2, O2, CO, HBr, and CO2. By tuning the relative phase, ϕ, between the two fields, we observe large forward-backward dissociation asymmetries. The largest asymmetries are obtained at the same values of ϕ for all species, suggesting a common dynamical mechanism. Following an independent phase calibration, the sign of the asymmetry appears to be opposite that expected from the standard enhanced ionization model.