Cellulose can be dissolved with another biopolymer in a protic ionic liquid and spun into a bicomponent hybrid cellulose fiber using the Ioncell® technology. Inside the hybrid fibers, the biopolymers are mixed at the nanoscale, and the second biopolymer provides the produced hybrid fiber new functional properties that can be fine-tuned by controlling its share in the fiber. In the present work, we present a fast and quantitative thermoanalytical method for the compositional analysis of man-made hybrid cellulose fibers by using thermogravimetric analysis (TGA) in combination with chemometrics. First, we incorporated 0–46 wt.% of lignin or chitosan in the hybrid fibers. Then, we analyzed their thermal decomposition behavior in a TGA device following a simple, one-hour thermal treatment protocol. With an analogy to spectroscopy, we show that the derivative thermogram can be used as a predictor in a multivariate regression model for determining the share of lignin or chitosan in the cellulose hybrid fibers. The method generated cross validation errors in the range 1.5–2.1 wt.% for lignin and chitosan. In addition, we discuss how the multivariate regression outperforms more common modeling methods such as those based on thermogram deconvolution or on linear superposition of reference thermograms. Moreover, we highlight the versatility of this thermoanalytical method—which could be applied to a wide range of composite materials, provided that their components can be thermally resolved—and illustrate it with an additional example on the measurement of polyester content in cellulose and polyester fiber blends. The method could predict the polyester content in the cellulose-polyester fiber blends with a cross validation error of 1.94 wt.% in the range of 0–100 wt.%. Finally, we give a list of recommendations on good experimental and modeling practices for the readers who want to extend the application of this thermoanalytical method to other composite materials.