We propose DepthTCM, a physics-aware end-to-end framework for depth map compression. In our framework of DepthTCM, the high-bit depth map is first converted to a conventional 3-channel image representation losslessly using a method inspired by a physical sinusoidal fringe pattern based profiliometry system, then the 3-channel color image is encoded and decoded by a recently developed Transformer-CNN mixed neural network architecture. Specifically, DepthTCM maps depth to a smooth 3-channel using multiwavelength depth (MWD) encoding, then globally quantized the MWD encoded representation to 4 bits per channel to reduce entropy, and finally is compressed using a learned codec that combines convolutional and Transformer layers. Experiment results demonstrate the advantage of our proposed method. On Middlebury 2014, DepthTCM reaches 0.307 bpp while preserving 99.38% accuracy, a level of fidelity commensurate with lossless PNG. We additionally demonstrate practical efficiency and scalability, reporting average end-to-end inference times of 41.48 ms (encoder) and 47.45 ms (decoder) on the ScanNet++ iPhone RGB-D subset. Ablations validate our design choices: relative to 8-bit quantization, 4-bit quantization reduces bitrate by 66% while maintaining comparable reconstruction quality, with only a marginal 0.68 dB PSNR change and a 0.04% accuracy difference. In addition, Transformer--CNN blocks further improve PSNR by up to 0.75 dB over CNN-only architectures.