The polarized longitudinal-transverse structure function sigma(LT') has been measured using the p((e) over right arrow ,e'pi(+))n reaction in the Delta(1232) resonance region at Q(2)=0.40 and 0.65 GeV2. No previous sigma(LT') data exist for this reaction channel. The kinematically complete experiment was performed at the Jefferson Lab with the CEBAF large acceptance spectrometer using longitudinally polarized electrons at an energy of 1.515 GeV. A partial-wave analysis of the data shows generally better agreement with recent phenomenological models of pion electroproduction compared to the previously measured pi(0)p channel. A fit to both pi(0)p and pi(+)n channels using a unitary isobar model suggests the unitarized Born terms provide a consistent description of the nonresonant background. The t-channel pion pole term is important in the pi(0)p channel through a rescattering correction, which could be model dependent.