We theoretically investigate the nonlinear response current of a two-dimensional system under an in-plane magnetic field. Based on the extended semiclassical theory, we develop a unified theory including both longitudinal and transverse currents and classify contributions according to their scaling with the relaxation time. Besides time-reversal-even contributions, we reveal a previously unknown time-reversal-odd contribution to the Hall current, which occurs in magnetic systems, exhibits band geometric origin, and is linear in relaxation time. We show that the different contributions exhibit different symmetry characters, especially in their angular dependence on the field orientation, which can be used to distinguish them in experiment. The theory is explicitly demonstrated in the study of the Rashba model. Our work presents a deepened understanding of nonlinear planar transport, proposes approaches to distinguish different contributions, and sheds light on possible routes to enhance the effect in practice.