We experimentally investigate the mixing/demixing dynamics of Bose-Einstein condensates in the presence of a linear coupling between two internal states. The observed amplitude reduction of the Rabi oscillations can be understood as a result of demixing dynamics of dressed states as experimentally confirmed by reconstructing the spatial profile of dressed state amplitudes. The observations are in quantitative agreement with numerical integration of coupled Gross-Pitaevskii equations without free parameters, which also reveals the criticality of the dynamics on the symmetry of the system. Our observations demonstrate new possibilities for changing effective atomic interactions and studying critical phenomena. PACS numbers: 32.80.Qk, 03.75.Kk, 03.75.Mn Critical phenomena appear in many areas of physics including phase transitions [1] and nonlinear dynamical systems [2]. Their experimental study requires a high level of control in order to quantitatively compare with theoretical predictions.Multi-component Bose gases featuring miscibilityimmiscibility transitions are prototypical systems for the investigation of critical phenomena due to unprecedented experimental control of the relevant parameters. Early experiments with Bose-Einstein condensates revealed demixing as well as mixing dynamics of two [3] and three-component [4] quantum fluids. In the latter, even spontaneous symmetry breaking and the corresponding pattern formation has been observed [5,6]. While these experiments have been performed with fixed interaction between the components, atomic systems also allow for the control of the interspecies interaction strength via a Feshbach resonance. This has enabled experiments, that clearly demonstrate miscibilityimmiscibility transitions [7] and study the two-component dynamics in detail [8][9][10]. An alternative approach for the control of interaction properties and the corresponding dynamics in one-dimensional systems has been demonstrated using state-selective transversal confinement [11]. Recently it has been shown, that the miscibility characteristics of spinor gases can be changed using Raman coupling [12].In the present letter, we experimentally investigate the theoretically predicted miscibility properties of two spin states in a Bose-Einstein condensate in the presence of linear coupling [13][14][15]. We report on the experimental observation of the demixing dynamics of the relevant spin states, i.e. dressed states. The (im)miscibility of the system manifests itself in the amplitude of the Rabi oscillations, which is given by the spatial overlap of the corresponding dressed states. Employing both sides of an interspecies Feshbach resonance, the miscible and immiscible regime of the uncoupled two-component system is accessible allowing to contrast the mixing/demixing dynamics to the coupled situation. As shown in the right panel of Fig. 1 the amplitude of the Rabi oscillations drops in the miscible regime (top) and remains close to unity for immiscible parameters (bottom). These observations indicate...