Ultrasound imaging is widely used in noninvasive medical diagnostics due to its efficiency, portability, and avoidance of ionizing radiation. However, its utility is limited by the quality of the signal. Signal-dependent speckle noise, signal-independent sensor noise, and non-uniform spatial blurring caused by the transducer and modeled by the point spread function (PSF) degrade the image quality. These degradations challenge conventional image restoration methods, which assume simplified noise models, and highlight the need for specialized algorithms capable of effectively reducing the degradations while preserving fine structural details. We propose DEMIX, a novel dual-encoder denoising framework with a masked gated fusion mechanism, for denoising ultrasound images degraded by mixed noise and further degraded by PSF-induced distortions. DEMIX is inspired by diffusion models and is characterized by a forward process and a deterministic reverse process. DEMIX adaptively assesses the different noise components, disentangles them in the latent space, and suppresses these components while compensating for PSF degradations. Extensive experiments on two ultrasound datasets, along with a downstream segmentation task, demonstrate that DEMIX consistently outperforms state-of-the-art baselines, achieving superior noise suppression and preserving structural details. The code will be made publicly available.