We consider the problem of estimating the direction of arrival of desired acoustic sources in the presence of multiple acoustic interference sources. All the sources are located in noisy and reverberant environments and are received by a microphone array. We propose a new approach for designing beamformers and DoA estimation methods based on the Riemannian geometry of the manifold of Hermitian positive definite matrices. Specifically, we show theoretically that incorporating the Riemannian mean of the spatial correlation matrices into frequently-used beamformers gives rise to spatial spectra that reject the directions of interference sources and result in a higher signal-to-interference ratio. We experimentally demonstrate the advantages of our approach in designing several beamformers and a recent DoA estimation method in the presence of simultaneously active multiple interference sources.