Depth perception of objects can greatly affect a user's experience of an augmented reality (AR) application. Many AR applications require depth matching of real and virtual objects and have the possibility to be influenced by depth cues. Color and luminance are depth cues that have been traditionally studied in two-dimensional (2D) objects. However, there is little research investigating how the properties of three-dimensional (3D) virtual objects interact with color and luminance to affect depth perception, despite the substantial use of 3D objects in visual applications. In this paper, we present the results of a paired comparison experiment that investigates the effects of object shape, fidelity, color, and luminance on depth perception of 3D objects in handheld mobile AR. The results of our study indicate that bright colors are perceived as nearer than dark colors for a high-fidelity, simple 3D object, regardless of hue. Additionally, bright red is perceived as nearer than any other color. These effects were not observed for a low-fidelity version of the simple object or for a more-complex 3D object. High-fidelity objects had more perceptual differences than low-fidelity objects, indicating that fidelity interacts with color and luminance to affect depth perception. These findings reveal how the properties of 3D models influence the effects of color and luminance on depth perception in handheld mobile AR and can help developers select colors for their applications.