Initial alignment for inertial navigation system (INS) has been widely used in practice under the assumption of Gaussian noises. In most previous works, nonlinear dynamics was ignored and the disturbances were merged into either a Gaussian or norm-bounded variable, where the Kalman filtering or robust filtering can be applied, respectively. In this article, the unmodelled nonlinear dynamics, drifts, parametric uncertainties, as well as other disturbances are considered simultaneously and are formulated into different types of uncertain disturbances described by the exo-system, stochastic and norm-bounded variable, respectively. A nonlinear initial alignment approach for INS is first presented based on a new disturbance attenuation and rejection filtering scheme against multiple disturbances. The INS error model with both nonlinear dynamics and multiple disturbances is established and the initial alignment problem is transformed into a robust nonlinear filter design problem for a class of nonlinear systems with multiple disturbances. In the proposed composite filtering approach, the drift filter is designed to estimate and compensate the inertial sensor drift. Mixed H-2/H-infinity filtering is designed to optimise the estimation error and attenuate the norm-bounded uncertain disturbances, respectively. Simulations for ground stationary base initial alignment of an INS are provided. Comparisons show that the concerned INS has the enhanced disturbance rejection and attenuation performance.