We demonstrate the simultaneous generation and internal interference of two second-order parametric processes in a single nonlinear quadratic crystal. The two-frequency doubling processes are Type 0 (two extraordinary fundamental waves generate an extraordinary second-harmonic wave) and Type I (two ordinary fundamental waves generate an extraordinary second-harmonic wave) parametric interactions. The phase-matching conditions for both processes are satisfied in a single periodically poled grating in LiNbO3 using quasi-phase-matching (QPM) vectors with different orders. We observe an interference of two processes, and compare the results with the theoretical analysis. We suggest several applications of this effect such as polarization-independent frequency doubling and a method for stabilizing the level of the generated second-harmonic signal.