You treat them as separate things. Kinda. You have the measurement mechanism and you have the unitary evolution mechanism. There are varying degrees of sophisti

You treat them as separate things. Kinda. You have the measurement mechanism and you have the unitary evolution mechanism. There are varying degrees of sophistication for modeling the measurement mechanism, and there's ways to have unitary evolution with simultaneous measurement, as well as weak measurement, and there's systems where you can probe the dynamics of a measurement. For instance, you can "watch" a quantum jump or even stop and reverse it (Z. K. Minev et. al. 2018). Generally these things are all modeled using the Stochastic Master Equation. In the end though, the SME is just unitary evolution of a small system coupled to a large markovian bath, with a Bayesian update added. In other words, one could derive the SME by taking an infinitesimal evolution of the unitary system (coupled to the bath) followed by an infinitesimal bayesian update, followed by unitary, followed by Bayesian update, etc. These things are all well covered by Gardiner Zoller 97, and Dan Steck's quantum optics notes, available at http://atomoptics-nas.uoregon.edu/~dsteck/teaching/quantum-optics/quantum-optics-notes.pdf http://atomoptics-nas.uoregon.edu/~dsteck/teaching/quantum-o... . Some would say that the SME is the fundamental thing, the Maxwell's equations of quantum information with measurement, and that the instantaneous measurement you may be familiar with is just a limit of the SME's evolution. Some might also say that the SME is a thing you derive from weakly coupling a stream qubits to a system and then performing hard, instantaneous measurement on those qubits. The math makes no distinction.