We have measured intrinsic tunneling spectra of charge density wave (CDW) materials NbSe3 and o-TaS3 in sub-micron scale mesa structures. Beyond the interband tunneling across the CDW gap, 2Δ, we observe intragap states at the voltage V≈ 2Δ/3 which we associate with creation of the amplitude soliton. The onset of the tunneling occurs only above a threshold voltage V_t≈ 0.1Δ followed by a quasi-periodic staircase spectrum. We interpret that behavior as the CDW phase decoupling between neighboring layers via the formation of a grid of dislocation lines. In NbSe3, the application of a high magnetic field (up to 27 T) yields a strong suppression of the tunneling density of states within the CDW gap indicating a possible field induced metal-insulator transition.