The ability to perform measurements between, or simultaneous with, the application of quantum gates is known as mid-circuit measurement. It is a key building block in many approaches to fault-tolerant quantum computation, such as for syndrome extraction, and necessary in paradigms such as measurement-based quantum computation. Here, we present our development of a modified version of quantum process tomography, and an interleaved benchmarking sequence that can be used to characterize the cross-chip impact of mid-circuit measurement. We demonstrate these techniques on superconducting multi-qubit devices available over the IBM cloud. *Research was sponsored by the Army Research Office and was accomplished under Grant Number W911NF-21-1-0002. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.