The ferromagnetically ordered state of random-field Ising systems for dimensionalities d<~3 is shown to be unstable with respect to domain formation, if the field-induced domain interface roughness is taken into account. For d=3, the interface exhibits a "wiggly" structure on all length scales intermediate between the correlation length and the domain size. This instability, which follows from the assumed random-field-induced roughening, makes the lower critical dimension, dl=3, consistent with the change of the effective dimensionality by 2 for the random-field model. Experimental consequences of these results are indicated. © 1981 The American Physical Society.