Low-cost, high-performance integration technologies are instrumental for active-passive integrated photonics devices. The monolithic integration of Al ₂ O ₃ and Si ₃ N ₄ is studied, enabling to combine the promising optical features of Si ₃ N ₄ with the excellent optical gain characteristics of rare-earth-ion doped Al2O3. The Al2O3 and Si ₃ N ₄ layers are separated by a thin SiO2 film and coupled by adiabatically width-tapered Al ₂ O ₃ and thickness-tapered Si ₃ N ₄ waveguides. In this paper, a detailed characterization of the couplers, as well as a study of the influence of the different design parameters and fabrication tolerances on the final device performance is presented. Test structures are characterized under transverse electric (TE) polarization. Measured loss per coupler is as low as 0.26 ± 0.03 dB at the wavelength of 1030 nm, and below 0.24 dB in the spectral window of 1460-1635 nm. Lateral misalignment of ±1 μm results in less than 0.6 dB increase of the coupler loss at 1030 nm, and the tolerance of misalignment goes up to 1.7 μm at the investigated longest wavelength of 1635 nm without introducing extra coupler losses. The reported integration technology paves the way toward a double-layer platform monolithically integrating Si ₃ N ₄ and rare-earth-ion doped Al ₂ O ₃ for active-passive photonic functionalities.