This article is concerned with the switched control of hybrid terrestrial and aerial quadrotors (HyTAQs) via stochastic hybrid fuzzy system methodology, in which the terrestrial and aerial mode switching is subject to a Markov process with lower-bounded sojourn time. For the first time, the bimodal nonlinear attitude dynamics of HyTAQs is analyzed and modeled based on the Takagi-Sugeno (T-S) fuzzy model, and switched fuzzy controllers are developed to stabilize the hybrid fuzzy system. The characteristic of state dimension switching caused by ground contact is modeled via the singular system presentation with mode-dependent singularity matrices, based on which numerically testable criteria of stability and stabilization in the stochastic sense are derived. Compared with the previous control approaches based on Markov jump systems, the proposed one is able to describe the deterministic dwelling duration in practice and integrate multiple subsystems with algebraic equations of different dimensions, while achieving lower conservatism. Illustrative examples are provided to demonstrate the effectiveness and potential of the designed variable-dimension fuzzy controllers.