Recently, a method of recording holograms of coherently illuminated three-dimensional scene without two-wave interference was demonstrated. The method is an extension of the coded aperture correlation holography from incoherent to coherent illumination. Although this method is practical for some tasks, it is not capable of imaging phase objects, a capability that is an important benefit of coherent holography. The present work addresses this limitation by using the same type of coded phase masks in a modified Mach-Zehnder interferometer. We show that by several comparative parameters, the coded aperture-based phase imaging is superior to the equivalent open aperture-based method. As an additional merit of the coded aperture approach, a framework for increasing the system's field of view is formulated and demonstrated for both amplitude and phase objects. The combination of high sensitivity quantitative phase microscope with increased field of view in a single camera shot holographic apparatus, has immense potential to serve as the preferred tool for examination of transparent biological tissues.