Spontaneous imbibition in porous media plays an important role in numerous industrial processes, but its underlying mechanisms are still poorly understood due to the complicated structure and multiple surface properties of natural porous media. In order to fill this gap, a quasi-three-dimensional color-gradient lattice Boltzmann model is applied to simulate the spontaneous imbibition in heterogeneous porous media micromodels, where the influence of viscosity ratio, tortuosity and mixed wettability is systematically investigated. Results show that the tortuosity has less influence on imbibition than the viscosity ratio, which leads to unstable displacement for viscosity ratios smaller than unity and to stable displacement for viscosity ratios greater than unity. By establishing the power-law relationship between wetting fluid saturation and time, it is found that the scaling exponent is not only affected by tortuosity, but also related to pore throat structure of the micromodel. In addition, the mixed wettability is found to significantly influence the stability of displacement, especially when the contact angle difference of two constituents is large. Specifically, the greater the mixing degree of two wettabilities, the more unstable the displacement will become, which results in an enhanced interface roughening. Accordingly, the scaling exponent deviates more from the prediction from the Lucas-Washburn equation. Due to the reduced connectivity of flow paths, the wetting fluid imbibition rate in mixed wettability condition is lower than that in uniform wettability condition, no matter whether the latter theoretically corresponds to a slow displacement or not.