Video generative models have achieved remarkable progress in synthesizing photorealistic video sequences. However, enabling broader and more creative downstream applications requires fine-grained instance-level video editing, including object insertion, object removal, and texture editing, which has emerged as a prominent yet challenging problem. Existing approaches either propose unified generative frameworks with only coarse semantic control, or design task-specific frameworks for individual editing tasks, limiting their flexibility and applicability across diverse real-world scenarios. To address these limitations, we propose AlbedoEdit, a unified generative video editing framework that jointly supports object insertion, object removal, and texture editing. Our key insight is that the intrinsic albedo map, which is invariant to lighting and contains no specularity, shadowing and inter-reflection effects, provides an effective and user-friendly mechanism for specifying fine-grained appearance edits. Built upon video foundation models, AlbedoEdit is fine-tuned to translate source RGB videos into edited RGB videos, conditioned on a user-edited first-frame albedo. Trained on a new paired synthetic dataset covering all three editing tasks, AlbedoEdit implicitly learns to harmonize edited contents and simulate complex real-world visual effects triggered by editing operations, including specular highlights, soft shadows, and mirror reflections. AlbedoEdit demonstrates superior performance over state-of-the-art video editing approaches, both qualitatively and quantitatively. Project webpage is https://vcai.mpi-inf.mpg.de/projects/AlbedoEdit/.