In this paper we propose a method of device position and orientation measurement in Two-Dimensional Communication networks. Two-Dimensional Communication technology enables devices placed on a thin sheet to achieve two key functions for ubiquitous networks, to communicate with each other and to receive electricity through the sheet wirelessly. For device localization on the sheet, the top conductor layer of the sheet has a 2D pattern of position codes. We develop a positioning sensor based on capacitance sensing that identifies the position code in the 2D conductor pattern under the sensor. We evaluate the accuracy of obtained position and orientation through an experiment using a prototype of our positioning sensor.