The possibility to reduce the effect of optical aberrations has been proposed in several publications on classical ghost imaging. The two-armed ghost-imaging systems make use of spatially incoherent illumination and point-by-point scanned intensity-correlation measurements in the arms. In this work, we introduce a novel ghostlike imaging method that uses a Mach-Zehnder interferometer and is based on optical-field interference instead of intensity correlations. The method allows us to obtain sharp images of microscopic objects even in the presence of severe aberrations that completely destroy the intensity-based image. Furthermore, pure phase objects can be imaged with micrometer-scale resolution in the presence of strong aberrations, which has not been demonstrated previously with a correlation-based imaging technique. In the setup, we use a light-emitting diode source and an ordinary camera as the only light detector. The imaging approach that we put forward in this work may find significant applications in advanced optical microscopy, optical coherence tomography, and a variety of interferometric sensors and detectors.