The parietal pleura is attached to the wall of the thoracic cavity and innervated by the intercostal nerves and phrenic nerve. Parietal pleura lines the thoracic wall, covers the superior surface of the diaphragm and separates the pleural cavity from the mediastinum.he parietal pleura is attached to the wall of the thoracic cavity and innervated by the intercostal nerves and phrenic nerve. Parietal pleura lines the thoracic wall, covers the superior surface of the diaphragm and separates the pleural cavity from the mediastinum.