Microtubule and actin are the two major cytoskeletal polymers that form organized functional structures in the interior of eukaryotic cells. Although the structural mechanics of the cytoskeleton has been extensively studied by direct manipulations in in vitro reconstitution systems, such unambiguous characterizations inside the living cell are sparse. Here, we report a comprehensive analysis of how the microtubule and actin cytoskeletons structurally respond to direct intracellular load. Ferrofluid-based intracellular magnetic tweezers reveal rheological properties of the microtubule complex primarily determined by filamentous actin. The strain fields of the microtubule complex and actin meshwork follow the same scaling, suggesting that the two cytoskeletal systems behave as an integrated elastic body. The structural responses of single microtubules to contact and remote forces further evidence that the individual microtubules are enclosed by the elastic medium of actin. These results, directly characterizing the microtubule and actin cytoskeletons as an interacting continuum throughout the cytoplasm, serve as a cornerstone for the physical understanding of intracellular organization.