To investigate three-dimensional flame structures of turbulent premixed flame experimentally, dual-plane planar laser induced fluorescence (PLIF) of CH radical has been developed. This dual-plane CH PLIF system consists of two independent conventional CH PLIF measurement systems and laser beam from each laser system are led to parallel optical pass using the difference of polarization, and CH PLIF is conducted in two parallel two-dimensional cross sections. The newly-developed dual-plane CH PLIF is combined with single-plane OH PLIF and stereoscopic particle image velocimetry (PIV) to clarify the relation between flame geometry and turbulence characteristics. The laser sheets for single-plane OH PLIF and stereoscopic PIV measurement are located at the center of two planes for CH PLIF. The separation between these two planes is selected to 500 ${mu}m$. The measurement was conducted in relatively high Reynolds number methane-air turbulent jet premixed flame. The experimental results show that various three-dimensional flame structures such as the handgrip structure, which has been shown by three-dimensional direct numerical simulations (DNS), are included in high Reynolds number turbulent premixed flame. It was shown that the simultaneous measurement containing newly-developed dual-plane CH PLIF is useful for investigating the three-dimensional flame structures. To analyze the flame structures quantitatively, the flame curvature was estimated by using the CH and OH PLIF images, and the probability density function (pdf) of the curvatures was compared with the results of DNS. It was revealed that the minimum radius of curvature of the flame front coincides with Kolmogorov length. However, the feature of pdf of the flame curvature is slightly different from result of DNS, if the curvature was estimated from experimental results in two-dimensional cross section. On the other hand, the feature of pdf of mean curvature that calculated from triple-plane PLIF results is similar to that obtained from three-dimensional DNS.