Previous implementations of structured-illumination microscopy (SIM) were slow or designed for one-color excitation, sacrificing two unique and extremely beneficial aspects of light microscopy: live-cell imaging in multiple colors. This is especially unfortunate because, among the resolution-extending techniques, SIM is an attractive choice for live-cell imaging; it requires no special fluorophores or high light intensities to achieve twice diffraction-limited resolution in three dimensions. Furthermore, its wide-field nature makes it light-efficient and decouples the acquisition speed from the size of the lateral field of view, meaning that high frame rates over large volumes are possible. Here, we report a previously undescribed SIM setup that is fast enough to record 3D two-color datasets of living whole cells. Using rapidly programmable liquid crystal devices and a flexible 2D grid pattern algorithm to switch between excitation wavelengths quickly, we show volume rates as high as 4 s in one color and 8.5 s in two colors over tens of time points. To demonstrate the capabilities of our microscope, we image a variety of biological structures, including mitochondria, clathrin-coated vesicles, and the actin cytoskeleton, in either HeLa cells or cultured neurons.