Placing your hand on the back of your husband's seat (or his on yours) when you are in
niddah is
not expressly prohibited. However, a husband and wife are only supposed to
eat together at the same table if there is some
heker (sign recognizable to them) that she is in
niddah. The concern is that eating in close quarters with one's spouse is an act of intimacy. Deliberately touching the back of a spouse's chair can be a comparable act of intimacy and physical closeness, especially if the movement of the hand or its effects can be felt, even indirectly, by the spouse in the chair.
For either a chair or a bed, incidental, unintentional touch, such as squeezing by the bed or chair or grasping at either for balance, would be permitted.