The symmetry between the field and atomic dipole squeezing(SFAS)has been exposed in the resonant JCM. The influence of some nonlinear interactions,including the nonresonant interaction, the virtual-photon processes,the intensity-dependent coupling and the interaction of a Kerr-like medium with the cavity on the SFAS has been discussed . At(2m+1)-quantum resonance,the relationship between the field and atomic squeezing has been examined.