If you look at Zarzuela Palace from above (via Google Earth or a similar satellite provider), you will see that the picture above is is the north (entrance) facade of the center block of the palace, which is flanked by two wings, each approximately the same size as the center block. One of those wings probably contains the private royal apartments, the other probably contains service areas.
Behind the palace (on the south side facing Madrid) are terraced gardens (the property sits on a hill), with an outdoor pool and tennis courts to the west edge. Just across the main driveway is what looks to me like 2 heliports. The palace itself is surrounded with a complex of other buildings, that look like greenhouses, and probably security and household staff quarters.
Just to the east, across the driveway, is the more modern residence of the Prince and Princess of Asturius. It has its own gardens and pool, and looks to the naked eye about half the size of the main palace.
Just northeast of Zarzuela, up another canyon, is the Palace of El Pardo, where Franco lived. From the satellite picture, that palace is totally surrounded by what looks like a village and a military base or other industrial looking buildings. Although El Pardo palace is bigger than Zarzuela, I can understand why the King and Queen chose not to move there. It seems to afford much less privacy than Zarzuela.