A N2-H2 capacitively coupled rf discharge has potential applications in etching of organic low dielectric constant (low-k) material for microelectronics technology. In this paper, we investigate the characteristic and electrical asymmetry effect (EAE) on the N2-H2 capacitively coupled plasma used for low-k material etching by particle-in-cell/Monte Carlo (PIC/MC) model, in which the two frequency sources of 13.56 MHz and 27.12 MHz are applied separately to the two electrodes in geometrically in symmetry. It is found that the plasma density profiles, the ion flux density profiles and the energy distribution of ion bombarding electrodes can be changed by adjusting the phase angle θ between the two harmonics. When the phase angle θ is 0°, the density of primary ion (H3+) near low frequencie electrode (LFE) (wafer) is smallest, whereas flux and average energy of ion (H+, H3+, H2+) bombarding LFE are biggest; if the phase angle θ is tuned from 0° to 90°, the dc self-bias increases almost linearly from -103 V to 106 V, ion flux bombarding the LFE decreases by ±18%, the maximum of the ion bombarding energy at the LFE decreases by a factor of 2.5. For the N2-H2 capacitively coupled rf discharge, for the case of two frequencies (13.56 MHz/27.12 MHz) applied separately to the two electrodes, can realize separate control of ion energy and flux via the EAE, and is generally in qualitative agreement with experimental and modeling investigation on the Ar and O2 plasma for a dual-frequency voltage source of 13.56 MHz and 27.12 MHz is applied to the powered electrode. This work supplies a references basis for experimental research and technology that the EAE on the H2-N2 plasmas is used for organic low-k material etching process.