Line-of-sight distortions of the cosmic microwave background (CMB), including gravitational lensing, cosmic birefringence, and patchy screening, encode crucial cosmological information. While quadratic estimators (QE) have been excellent tools for extracting these signals, they become suboptimal for current- and next-generation CMB surveys, failing to maximize signal-to-noise and suffering from bias contamination that standard bias-hardening techniques cannot mitigate. We present a joint maximum a posteriori framework that simultaneously reconstructs multiple distortion fields while explicitly accounting for their mutual contamination. For cosmic birefringence searches, our method achieves up to 2.5 times improvement in reconstruction noise compared to the QE, while significantly reducing CMB lensing-induced biases up to a factor of 5. These gains in lensing biases manifest not only in deep polarization surveys like CMB-S4 and SPT-3G, but also in higher-noise experiments like Simons Observatory, where our method reduces lensing-induced biases by a factor of two thanks to the power of delensing. Our code provides a first step to robust analyses of CMB secondary anisotropies, their cross-correlations with large-scale structure, and ultimately enabling more sensitive searches for primordial $B$-modes.

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• Cosmic microwave background
• Large scale structure of the Universe
• Primordial magnetic fields