This article completes the proof of theLp-boundedness of bilinear operators associated to nonsmooth symbols or multipliers begun in Part I, our companion article [8], by establishing the corresponding Lp-boundedness of time-frequency paraproducts associated with tiles in phase plane. The affine invariant structure of such operators in conjunction with the geometric properties of the associated phase-plane decompositions allow Littlewood–Paley techniques to be applied locally, i. e., on trees. Boundedness of the full time-frequency paraproduct then follows using ‘almost orthogonality’ type arguments relying on estimates for tree-counting functions together with decay estimates.