Probabilistic error cancellation (PEC) is a practical error-mitigation technique to obtain accurate, bias-free estimates of observable expectation values. The procedure learns the noise associated with ideal unitary gates and implements a noise inversion via probabilistically sampling Paulis from an appropriately constructed inverse distribution. In this work, we extend the PEC framework to move beyond ideal unitary gates and implement noise learning and mitigation for circuits consisting of mid-circuit measurements, and classically controlled unitary operations ('feedforward'). Our work introduces a novel approach to learning and error mitigation for circuits with non-unitary, mid-circuit operations as well as characterizing the impact of these operations on active, unmeasured qubits. We discuss the learned measurement model for mid-circuit measurements and feedforward, and comparatively analyze several methods for constructing and solving the underlying inverse problem. The learning protocol retains the scalability of the approach introduced in [arXiv:2201.09866] and can be extended to circuits with large qubit count. These advances enable us to demonstrate PEC on measurement-based circuits.