Three-dimensional weaving, knitting, or braiding tools may be used to create three-dimensional fabric (24) with internal pockets (56). The pockets (56) may be shaped to receive electrical components such as switch electrodes (46A, 46B) for a switch (18). The fabric (24) may have adjacent first and second layers that are interposed between the switch electrodes (46A, 46B). The switch electrodes (46A, 46B) may be biased apart using magnets (46A-1, 46B-1) or other biasing structure. In a region of the fabric (24) that overlaps the first and second switch electrodes (46A, 46B), the first and second layers of fabric may be disconnected from each other. This allows the first and second layers to pull away from each other so that the electrodes (46A, 46B) are separated by the biasing force from the biasing structure. The switch (18) can be closed by pressing the electrodes (46A, 46B) together.