Quantitative phase imaging (QPI) is a label-free technique that provides optical path length information for transparent specimens, finding utility in biology, materials science, and engineering. Here, we present quantitative phase imaging of a 3D stack of phase-only objects using a wavelength-multiplexed diffractive optical processor. Utilizing multiple spatially engineered diffractive layers trained through deep learning, this diffractive processor can transform the phase distributions of multiple 2D objects at various axial positions into intensity patterns, each encoded at a unique wavelength channel. These wavelength-multiplexed patterns are projected onto a single field-of-view (FOV) at the output plane of the diffractive processor, enabling the capture of quantitative phase distributions of input objects located at different axial planes using an intensity-only image sensor. Based on numerical simulations, we show that our diffractive processor could simultaneously achieve all-optical quantitative phase imaging across several distinct axial planes at the input by scanning the illumination wavelength. A proof-of-concept experiment with a 3D-fabricated diffractive processor further validated our approach, showcasing successful imaging of two distinct phase objects at different axial positions by scanning the illumination wavelength in the terahertz spectrum. Diffractive network-based multiplane QPI designs can open up new avenues for compact on-chip phase imaging and sensing devices.